For the following exercises, use a calculator to find the length of each side to .....A 200-foot tall monument is located in the distance. From a window in a building, a person determines...

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A 200-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 15°, and that the angle of depression to the bottom of the tower is 2°. How far is the person from the monument?

Expert Solution

The problem can be described by the figure below.

Point A is the point of observation. C denotes the bottom of the monument and B the top. The distance AD is to be calculated whereas the length BC is the height of the monument that is 200 feet.

The height of the monument is the sum of lengths BD and CD which are related to the distance AD by the definition of the tangent of an angle in a right angled triangle.

tan A = length of side opposite to A/length of side adjacent to A

Thus,

tan 15° = BD/AD, tan2° = CD/AD

The length BC is thus,

BC = BD + CD

200 = ADtan15° + ADtan2°

AD = 200/(tan15° + tan2°)

= 660.3494

The distance between the person and the monument is thus approximately 660.35 feet.

Junaid answered 1 year ago

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