You are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82°. If the total height of the building is another 123 meters above the 86th floor, what is the total height of the building?

Question

Mathematics

Tater

15 August, 11:49

You are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82°. If the total height of the building is another 123 meters above the 86th floor, what is the total height of the building?

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Hassan Gould · Answer 1

base, b = 45m

angle of elevation, aoe = 82deg

height at 86th floor, h1

height above 86th floor, h2 = 123m

total height, h = h1 + h2

using

tan (aoe) = h1/b

=" h1 = tan (aoe) * b = tan 82 x 45 = 320.2

h = h1 + h2 = 320.2 + 123 = 443.2m