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

Answer:

640.919 feet

Step-by-step 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

$tan 37 =\frac{x}{400} \\x=400 tan 37 = 301.422'$

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

$tan 67 = \frac{301.422+y}{400} \\y = 400 tan 67 -301.422 = 640.919$