Question

An antenna stands on top of a 160 ft. building. From a point on the ground 118 ft. from the base of the building, the angle of elevation to the top of the antenna is 58 degrees. Find the height of the antenna.

Answer 1

Answer: the height of the antenna is 21

Step-by-step explanation:

The diagram illustrating the scenario is shown in the attached photo. A right angle triangle ABC is formed.

Let x represent the height of the antenna. Therefore, the height of the building and the antenna would be (160 + x) feet

We would determine (160 + x) feet by applying the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side

Therefore

Tan 58 = (160 + x)/118

160 + x = 118tan58

160 + x = 118 × 1.6003

160 + x = 188.8354

x = 188.8354 - 160

x = 20.8354

Approximately 21 feet