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.

Question

Mathematics

String Bean

16 October, 00:46

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.

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Daniella Arias · Answer 1

19.72 ft

Step-by-step 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