Question

You are measuring the height of a statue. You stand 10 feet from the base of the statue. You measure the angle of elevation from the ground to the top of the statue to be 76º. Find the height h of the statue to the nearest foot.

Answer 1

Answer: h = 40 feet

Explanation:

Hi, to answer this question we have to apply the trigonometric functions.

Since the situation is represented by a right triangle (see attachment) we have to apply:

tan (angle ) = opposite / adjacent

Replacing with the values given:

tan 76 = h / 10

Solving for h

tan76 x 10 = h

40.10 feet = h

h = 40 feet

Feel free to ask for more if needed or if you did not understand something.

Answer 2

The height of the status to nearest foot is 40feet

Explanation:

The set up will give us a tight angled triangle with the angle of elevation facing the height of the status and the base of the status being the adjacent side.

Using the trigonometry identity (SOH CAH TOA) to tackle the problem:

Given angle of elevation θ =76°

Base of the status = 10feet = Adjacent

Height of the status = x = opposite

According to TOA defined as:

Tanθ = Opposite/Adjacent

Tan76° = x/10

x = 10tan76°

x = 40feet