Question

The drawing shows a person looking at a building on top of which an antenna is mounted. The horizontal distance between the person’s eyes and the building is 83.2 m. In part a the person is looking at the base of the antenna, and his line of sight makes an angle of 33.3 with the horizontal. In part b the person is looking at the top of the antenna, and his line of sight makes an angle of 35.7o with the horizontal. How tall is the antenna?

Answer 1

Consider the triangles formed by the lines of sight in parts a and b. In part a, the distance from the horizontal to the base of the antenna is 82.0*tan31.0º; in part b, the distance from the horizontal to the top is 82.0*tan34.2º. The antenna height is the difference between these 

h = 82.0*tan34.2º - 82.0*tan31.0º = 82.0*(tan34.2º - tan31.0º) = 6.46 m