Question

A 40-foot y’all monument sits on top of a hill. Eye is standing at a point on the hill and observes the top of the monument at an angle of elevation of 50 degrees and the bottom of the monument at an angle of elevation of 22 degrees. Find the distance Pete must climb to reach the monument.

Answer 1

54.8 feet

Explanation:

We assume that the distance of interest is the direct line distance from the observation point to the bottom of the monument, segment PH in the diagram below.

This can be found using the Law of Sines.

∠PMH is the complement of the angle of elevation to the top of the monument, so is 40°.

∠MPH is the difference in the angles of elevation, so is 28°.

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The Law of Sines tells us the ratio of side lengths is the same as the ratio of the sines of the opposite angles, so ...

PH/MH = sin(∠PMH)/sin(∠MPH) = sin(40°)/sin(28°)

Multiplying by MH, we can find the length of PH:

PH = (40 ft)(sin(40°)/sin(28°)) ≈ 54.7669 ft

PH ≈ 54.8 ft . . . . the distance Pete must climb to reach the monument.