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?

Question

Mathematics

Mario Horn

28 October, 05:23

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?

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Lozano · 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