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
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....!!!!!