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.

The height of the antenna on top of the buildings is 28.02 feet.

The situation form 2 right angle triangle.

Therefore,

The base of the building to the location is the adjacent side of the triangle.

Using trigonometric ratio, the height of the building can be found as follows:

tan 40° = opposite / adjacent

tan 40° = h / 300

height of the building = 300 × tan 40° = 251.729889353 = 251.73 feet

The height of the building plus the antenna can be found as follows:

tan 43° = h / 300

height of the building plus the antenna = 300 × tan43

height of the building plus the antenna = 279.754525841 = 279.75

Height of the antenna =  279.75 - 251.73 = 28.02 feet

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Height of the antenna = 28 ft (Approx)

Given:

Length of base = 300 ft

Angle of elevation to the building = 40°

Angle of elevation to the antenna = 43°

Find:

Height of the antenna

Computation:

Using trigonometry function:

Tan40° = Height of building / Length of base

Height of building = 251.73 ft

Tan43° = [Height of building + Height of the antenna]  / Length of base

0.9325 = [251.73 + Height of the antenna] / 300

Height of the antenna = 28.02 ft

Height of the antenna = 28 ft (Approx)

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