Question

An observer, who is standing 47 m from a building, measures the angle of elevation of the top of the building as 30˚. If the observer’s eye is 167 cm from the ground, what is the exact height of the building?

Answer 1

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Answer:

28.81 m

Explanation:

The tangent relation can help find the height of the building above the observer's eye.

Tan = Opposite/Adjacent

Opposite = Adjacent·Tan

above eye height = (47 m)(tan 30°) ≈ 27.14 m

Adding this to the eye height gives the height of the building above the ground where the observer is standing.

27.14 m + 1.67 m = 28.81 m

The height of the building to the nearest centimeter is 28.81 meters.