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
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.
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
