Question

the height of building AB is 100 feet. The height of building CD is 50 feet. The buildings are on opposite sides of an avenue that is 90 feet wide. From a point E on the avenue, the measure of the angle of elevation to B is 55 degrees. Determine the distance from E to A to the nearest foot

Answer 1

tan 55° = Opposite leg / adjacent leg
tan 55° = AB / AE
tan 55°=100 feet / AE
Solving for AE:
AE tan 55° = 100 feet
AE = 100 feet / tan 55°
AE= 100 feet / 1.428148007
AE=70.02075380 feet
Rounded to the nearest foot:
AE=70 feet

Answer: The distance from E to A is 70 feet

Answer 2

We can ignore the second building, since all we need is the distance from E to A. By SOH-CAH-TOA, the opposite to angle E is AB, and the adjacent side is AE.
tan E = AB / AEtan(55) = 100/AEAE = 100/tan(55) = 70.02 feet.