Trig formulas in Excel

[RCH]

Not knowing Trig is rough sometimes. Appreciate your help for the following. I will incorperate solution into a function later.

Thanks,

Associated images are http://www.alibre.com/forum/viewtopic.php?f=9&t=10979&p=65310#p65310

<TABLE style="WIDTH: 395pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0 cellPadding=0 width=527><COLGROUP><COL style="WIDTH: 26pt; mso-width-source: userset; mso-width-alt: 1280" width=35><COL style="WIDTH: 81pt; mso-width-source: userset; mso-width-alt: 3949" width=108><COL style="WIDTH: 48pt" span=6 width=64><TBODY><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; WIDTH: 26pt; HEIGHT: 15pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20 width=35></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: #dbe5f1; WIDTH: 81pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl74 width=108>A</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>B</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>C</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>D</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>E</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>F</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #dbe5f1; WIDTH: 48pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 width=64>G</TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>1</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl65 colSpan=3>Variable (as shown in image 1)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>2</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>Wall 180Offset</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>1.250</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=5>(Center of wall at 180 degrees - "left" - of origin)</TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>3</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>Wall Dia</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>8.000</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>4</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>InnerCircDia</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>0.500</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>5</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>OuterCirDia</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>0.500</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>6</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>CirSepLth</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>1.000</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=4>(Inner Circle to Outer Circle - ctr to ctr)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>7</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl66></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>8</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl65 colSpan=4>Continously variable (as shown in image 1)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>9</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>SweepAngle</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>90.000</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=4>(from origin - as shown in sketch)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>10</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl66></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>11</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl66></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>12</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl76 colSpan=7>"Inner Line"</TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>13</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=6>a line drawn from the origin, to the tangency of the inner circle to </TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>14</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=5>an inner wall (circle) drawn concentric to Wall 180offset</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>15</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>16</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl71>results</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl72 colSpan=4>(example results from measuring)</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>17</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl70>@90 deg</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl70>@135</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl70>@180</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl70>@235</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>18</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>InnerLineLength</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>3.553</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>4.527</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>5.000</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>4.323</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>19</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>InnerLineAngle</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>88.560</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>134.200</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>180.000</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>235.960</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>20</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69></TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>21</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>OuterLineLength</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>4.060</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>5.040</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>5.500</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>4.841</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>22</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl68>OuterLineAngle</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>90.980</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>135.560</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>180.000</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl69 align=right>234.320</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>23</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>24</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl75 colSpan=5>Rotation of the inner and outer circles is constrained to </TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>25</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl75 colSpan=6>the midpoint of the "Wall 180Offset" and straight line from origin</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>26</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl75 colSpan=4>through midpoints of the smaller circles.</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>27</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>28</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" colSpan=7>The resulting circles are "traced" by the smaller inner and outer circles inside </TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>29</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8; mso-ignore: colspan" class=xl75 colSpan=7>and outside the "Wall 180Offset" - and fluctuate in radius as the angle sweeps </TD></TR><TR style="HEIGHT: 15pt" height=20><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #dbe5f1; HEIGHT: 15pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl73 height=20>30</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8">around.</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8"></TD></TR></TBODY></TABLE>

 

[sijpie]

It's a bit unclear what you need. "help for the following" But there is no 'following', just a piece of spreadsheet.

What exactly do you need help with? With formulas? something else?

Formulas for what exactly? be accurate, please, in your requests.

 

[RCH]

Requesting the excel solution for the length and angle of two lines, such that I can change variables to experiment with variations.

Can you see the link and the sketches at the link location in the first post - at the top above the spreadsheet example? If not I will need to fix that. I can add other views if wanted. Here is my attempt to describe a word problem.

On a 2D plane there is a point of origin, and to the left (1.25 inches at 180 degrees) is the center point of a circle with an 8 inch diameter (in this example).

A straight line (a ray lets say) extends from the origin - for a start say it is straight up at 90 degrees as in the 2nd image. On this line are two small circles (both .500 here, but not always) passing through the center of the circles.

The two small circles are fixed 1 inch apart here - from center to center.

As the angle of the line from origin changes the circles are rotated around the origin.

The length of the line segment from the origin to intersection of the 8 inch circle, which is midway between the two small circles, is defined by the point that exists halfway between the two small circles. This point is coincident or fixed to follow the line of the offset circle that is shown as 8 inches in diameter.

A new circle can then drawn from the center of the 8 inch circle. This new circle is tangent to the outside of the .500 circle closest to the origin.

Line 1 - A line is then drawn from the origin to this tangent point on the small circle. Show formulas for length and angle of this line.
​

Another new circle can then drawn again from the center of the 8 inch circle. This new circle is tangent to the inside of the .500 circle furthest to the origin.

Line 2 - Another line is then drawn from the origin to this tangent point on the small circle. Show formulas for length and angle of this line.
​

Of course no drawing of lines is required, although Excel can do that .

As the line or ray from origin changes angle, the two large circles created will vary in diameter because as the angle of the line from origin changes, the distance and relative position of the small circles to the large 8 inch circle shifts, and I need to plot it.

The piece of spreadsheet is just a help to whoever works on this. A starting point is the least I can do.

I hope the word problem description is clear. Let me know - it is not my field . If this is tough for you, it is torture for me.

Thank You

 

[RCH]

Perhaps I should also say that I need the intermediate formulas to get to the line and angle calculations.

 

[RCH]

If it helps - the distance from the origin to the 8 inch circle at 90 degrees is measured as 2.727 inches (using a sketch in Alibre).

Thanks again,

(I hope someone here is good at trig )

 

[Taul]

Ok, curiosity has got the better of me; What the hell is it?

It looks like a cam follower of some kind, am I right or am I barking up the wrong tree.

If the arm with the two small circles sweeps around to the left, the distance between the two small circles will change, ok I know you are interested in the length of the arm to the tangent point but it looks like there are bits of the scenario missing. It would help me to understand if you explain what this machine or mechanism actually does and what it is used for.

BTW, does the arm make a complete 360 rotation or is it just limited to a 135 degree rotation.

 

[RCH]

It is a curiosity, but lawyers, confidentiality, a new product and all, you know? Wrong tree, right forest.

The distance between the two small circles doesn't actually change itself mind you - just the relative distance between points on the two large circles (oblongs?) that will be mapped from the length and angle of the two lines in question.

A generic spreadsheet solution will take any angle. I will break out what works to VB or whatever and put what goes where.

It is a W.I.P., but when everything is done I can send you literature about it some day.

Thanks

 

[RCH]

If anyone wants to work on this, post a message, I don't want everyone jumping on it at the same time .

If no one speaks up by Sunday I'll try the MrExcell consulting service.

(which proves Excel / VB is easier than trig)

 

[RCH]

Btw

- I would try the math forums out there, but they don't "speak" excel. But, if you know one that does, post a link.

 

[Taul]

The system does not appear to work, I am basing this on your explanation of the two small circles remaining in line with the arc of rotation. Yet the main 8 inch circle has two concentric circles indicating the contact point of the two smaller circles.

The only way the two concentric circles could remain “concentric, is if the two small circles had a pivot point on the main (blue) 8 inch circle. Allowing them to continuously point to the centre of the 8 inch circle.

If they remain “fixed” and pointing toward the centre of rotation, the gap between the smaller circles (indicated by the dotted lines either side of the blue 8 inch circle) would be variable.

Could you confirm there is a pivot point between the two smaller circles.

Sorry about all the questions but I need to understand the geometry before the trig can start