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

#1**+1 **

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....!!!!!

CPhill
Apr 5, 2017