Question

A person is standing 200ft from a tower. She can see the top of the tower at a 42 degree angle of elevation. Her eyes are 5ft above the ground*. What is the height of the tower. Round your answer to the nearest foot

A. 154ft
B. 149ft
C. 185ft

Answer 1

C. 185 ft

Explanation:

The work is in the attached picture file, if you need it. Basically the question sets up a right triangle, for which the base is 200 and the height is the goal that you are solving for. It is given that the angle between hypotenuse and base is 42 degrees. For this you use tangent to say that

tan(42) = h / 200

200 tan (42) = h

h = 180 feet.

But then you must remember that this triangle starts 5 feet off of the ground. So you add the 5 feet and get 185 feet as the height of the tower.