Question

From her eye, which stands 1.75 meters above the ground, Myesha measures the angle of elevation to the top of a prominent skyscraper to be 19^{\circ}

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. If she is standing at a horizontal distance of 337 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary

Answer 1

117.79 m

Explanation:

You have an observer 337 m from a skyscraper who measures the angle of elevation from a point 1.75 m above the ground to be 19°. You want to know the height of the skyscraper.

Tangent

The tangent relation tells you ...

Tan = Opposite/Adjacent

Solving for the side opposite the angle, we get ...

Opposite = Adjacent · Tan

Application

In this scenario, the height of the building above the eye height is ...

height above eyes = (337 m)(tan 19°) = 116.038 m

Then the height of the building is ...

skyscraper height = eye height + height above eyes

skyscraper height = 1.75 m + 116.038 m = 117.788 m

The height of the skyscraper is about 117.79 meters.