The distance to the sun is approximately 93 million miles If

The distance to the sun is approximately 93 million miles. If the angle subtended by the sun from an observer\'s eye on earth is approximately .0093 radians, find the approximate diameter of the sun. Round to the nearest mile

Solution

0.0093 radian = 0.5 degree

Diameter is 2 times Radius
Radius = distance times tangent(angle)
2*93e6*tan(0.5) = 1,623,200 miles

Or the small angle approximation
Angle=Radius/distance ==> Radius=Angle*distance
0.00872*93e6 = 811,600 miles (For this approximation, the angle MUST be in radians! check this out - the tan of 0.00872 = 0.00872)
Diameter = 2* Radius = 1,623,200 miles