Question

From the earth, the moon subtends an angle of approximately 0.5°. If the distance to the moon is approximately 240,000 miles, find an approximation for the diameter of the moon accurate to the nearest hundred miles. (See Example 4 and the discussion that precedes it.)

Answer 1

2100 miles.

Explanation:

Given:

Diameter to the moon = 240000 miles

∅ = 0.5 °

The subtended angle by an arc is given as:

S = r∅

Where

r = radius of the circle

Therefore,

D = 240,000 x (0.5 x π rads)/180

= 2094 miles

= 2100 miles.