There is a tall antenna on the top of a building When a pers

There is a tall antenna on the top of a building. When a person stands 200 feet away from the building, the angle of elevation to the top of the building is 68.2 degree, and the angle of elevation to the top of the antenna is 69.3 degree. Sketch a diagram showing the building, the antenna, the angles of elevation and the person. Find the height of the antenna.

Solution

Distance of person from building = D = 200 feet

Height of building = h = D*tan68.2 = 200*tan68.2 = 500 feet

Height of the top of antenna from base = H = D*tan69.3 = 200*tan69.3 = 530 feet

Height of Antenna = H – h = 530 – 500 = 30 feet