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

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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

Answers

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 legtan 55° = AB / AEtan 55°=100 feet / AESolving for AE:AE tan 55° = 100 feetAE = 100 feet / tan 55°AE= 100 feet / 1.428148007AE=70.02075380 feetRounded to the nearest foot:AE=70 feetAnswer: The distance from E to A is 70 feet

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