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?

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

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