Question

There is an antenna on the top of a building. From a location 400 feet from the base of the building, the angle of elevation to the top of the building is measured to be 37°. From the same location, the angle of elevation to the top of the antenna is measured to be 40°. Find the height of the antenna. (Round your answer to three decimal places.)

Answer 1

640.919 feet

Explanation:

Given that there is an antenna on the top of a building. From a location 400 feet from the base of the building, the angle of elevation to the top of the building is measured to be 37°. From the same location, the angle of elevation to the top of the antenna is measured to be 40°

Let the height of building be x and that of antenna be y.

Then by considering right angle formed by horizontal line, vertical height and line made by eye contact we have

`tan 37 =(x)/(400) \\x=400 tan 37 = 301.422'`

Next considering the height with antenna included we get total height
`=x+y\\=301.422+y`

`tan 67 = (301.422+y)/(400) \\y = 400 tan 67 -301.422 = 640.919`