Question

A 175-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is 17°, and that the angle of depression to the bottom of the tower is 4°. How far is the person from the monument?

Answer 1

466 ft

Explanation:

You want the distance to a monument if the angle to the top of the 175 ft monument is 17°, and the angle to its bottom is 4°.

Tangent

The tangent relation is ...

Tan = Opposite/Adjacent

Then the side Opposite the angle is ...

Opposite = Adjacent·Tan

Application

The distance from the level of the observer to the top of the monument is ...

(distance above) = (distance to the monument) · tan(17°)

And the distance from the level of the observer to the bottom of the monument is ...

(distance below) = (distance to the monument) · tan(4°)

The sum of these is the height of the monument:

175 ft = (distance above) +(distance below)

175 ft = (distance to the monument) · (tan(17°) +tan(4°))

distance to the monument = (175 ft)/(tan(17°) +tan(4°)) ≈ 466 ft

The person is about 466 feet from the monument.

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The second attachment shows a diagram of the problem.