There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the....For the following exercises, use a calculator to find the length of each side to four decimal places.

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

There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the top of the building is measured to be 40°. From the same location, the angle of elevation to the top of the antenna is measured to be 43°. Find the height of the antenna.

Solutions

Expert Solution

The problem can be described by the following figure.

Point A is the point of observation. Point B is the base of the building. Point C is the top of the antenna whereas Point D is the top of the building. It is given that the angle ∡DAB is 40 degrees and the angle ∡CAB is 43 degrees. The distance AB is 300 feet. The height of the antenna, CD is to be found.

The heights BD and BC are related to the distance AB 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 40° = BD/AB, tan 43° = BC/AB

The height CD is:

CD = BC – BD

= AB(tan43° – tan40°)

= 28.0246

The height of the antenna is thus approximately 28.02 feet.

Junaid answered 1 year ago

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