Question

A person standing 130 feet away from the foot of a tall building must look up at an angle of 30° to see the top of the building. There is a radio antenna on the top of the building. The angle of elevation of the top of the radio antenna is 45°. Write an equation to determine the height of the radio antenna.

a) h = 130 tan(30°)
b) h = 130 tan(45°)
c) h = 130 tan(15°)
d) h = 130 tan(60°)

Answer 1

To find the height of the radio antenna on top of the building, the correct equation is h = 130 tan(45°), as the angle of elevation to the antenna is 45°.

Step-by-step explanation:

The question is asking to find the height of a radio antenna situated on top of a building, requiring the understanding of trigonometric functions specifically the tangent function in relation to an angle of elevation. Given the angle of elevation to the top of the building is 30° and the distance from the building is 130 feet, the height of the building can be determined using the equation h = 130 tan(30°). However, the angle of elevation to the top of the radio antenna is given as 45°, implying the height of the antenna above the building can be calculated using a different tangent function, h = 130 tan(45°). Therefore, the correct equation to determine the height of the radio antenna is option (b).