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Find the angular size of a circular object with a 3 in diameter viewed from the distance of 6 yards.

I know to find this use the formula angular size = physical size X 360 degree/ 2x3.14xdistance just don't understand how to put it in the calculator 

Guest Apr 5, 2017
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I'll have to solve this in the way I know how.....

 

Convert  6 yards to inches  =  6 * 3 * 12   =  216 inches

 

One line drawn from the viewing point to the circle will form a tangent to the circle......and this will form one leg of a right triangle with the hypotenuse = the viewing distance + 1/2 the diameter  = 217.5 inches...and from the viewing point, the opposite side of this triangle will =  1/2 the diameter  = 1.5 inches

 

So.....1/2 of the viewing angle can be expressed as

 

sin θ  =  1.5 / 217.5

sin-1 (1.5 / 217.5)  = .3951°

 

So.....the remaining angle in this triangle is 1/2 of the angular size we are looking for =

 

[ 180  - 90 - .3951]  = 89.6049 °

 

And twice this is the angular size  = 179.2098°

 

This makes sense......we are viewing a relatively small circle from a relatively large distance so we should be able to see almost 1/2 of the circle....!!!!! 

 

 

cool cool cool

CPhill  Apr 5, 2017
edited by CPhill  Apr 5, 2017

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