Asurveyor 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?

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

Really long apparently