Question

For the following exercises, use a calculator to find the length of each side to four decimal places.

A 400-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 18°, and that the angle of depression to the bottom of the monument is 3°. How far is the person from the monument?

Answer 1

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 400 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 A/length of side adjacent to A

Thus,

tan 18° = BD/AD, tan3° = CD/AD

 

The length BC is:

  BC = BD + CD

400 = ADtan18° + ADtan3°

 AD = 400/(tan18° + tan3°)

      = 1060.0.871

 

The distance between the person and the monument is thus approximately 1060.09 feet.

The distance between the person and the monument is thus approximately 1060.09 feet.