Question

a surveyor standing 64 meters from the base of a building measures the angle to the top of building and finds it to be 39 degrees . the surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48 degrees. how tall is the radio tower?

Answer 1

The distance of the observer and height of the building form a right angle triangle. Using:
tan∅ = height/base
We calculate the height of the building:
height = 64tan(39)
height = 51.8 meters

The second angle is obtained when the height of both the building and tower are used:
Height(building + tower) = 64tan(48)
51.8 + tower height = 71.1
tower height = 19.3 meters