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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 85.5 m. In part a the person is looking at the base of the antenna, and his line of sight makes an angle of 38.9o 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 41.6o with the horizontal. How tall is the antenna?

Answer :

height of building (h1):
tan(38.9°) = opposite / adjacent
tan(38.9°) = h1 / 85.5
85.5 tan(38.9°) = 68.990 (5sf)

height of building with antenna (h2):
tan(41.6°) = opposite / adjacent
tan(41.6°) = h2 / 85.5
85.5 tan(41.6°) = 75.910 (5sf)

height of antenna (h2 - h1)
75.910 - 68.990 = 6.92m

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