Question

A statue is mounted on top of a 42 foot hill. From the base of the hill to where you are standing is 73 feet and the statue subtends an angle of 10.3° to where you are standing. Find the height of the statue.

Answer 1

19.72 ft

Explanation:

You know the tangent of an angle is the ratio of the opposite side to the adjacent side of the right triangle. So, the angle α to the bottom of the statue is ...

tan(α) = (42 ft)/(73 ft)

α = arctan(42/73) ≈ 29.914°

Then the angle to the top of the statue is ...

β = 10.3° +29.914° = 40.214°

The same tangent relationship tells us the height to the top of the statue from the base of the hill is ...

tan(β) = (height to top)/(73 ft)

Multiplying by 73 ft gives ...

height to top of statue = (73 ft)·tan(40.214°) = 61.72 ft

So, the height of the statue is the difference between the heights of its top and its base:

statue height = 61.72 ft - 42 ft

statue height = 19.72 ft