Question

A contractor is checking the height of the frame for a building his company is constructing. He stands at some distance from the building and measures the angle of elevation to be 73 degrees. He moves back 10 feet and measures the angle to be 68 degrees. How tall is the building?

Answer 1

about 102 feet

Explanation:

From the definition of the cotangent function, we can write ...

h·cot(α1) = d1

h·cot(α2) = d2

Where h is the building height and (α1, d1), (α2, d2) are (elevation angle, distance from the building) for the two cases.

We have d2 - d1 = 10 ft, so ...

h(cot(68°) -cot(73°)) = 10 ft

h = (10 ft)/(cot(68°) -cot(73°)) ≈ (10 ft)/(0.404026 -0.305731) ≈ 101.73 ft

The building is about 102 feet tall.