You are standing 45 meters from the base of the Empire State Building. You estim

Question

You are standing 45 meters from the base of the Empire State Building. You estimate the angle of elevation to the top of the 86th floor (the observatory) is 82 degrees. The total height of the building is another 123 meters above the 86th floor. (a) What is the approximate height of the building? (b) One of your friends is on the 86th floor. What is the distance between you and your friend? A Ferris Wheel 40 feet in diameter makes one counterclockwise revolution every 30 seconds, if the center of the wheel is 25 feet above the ground, how long after reaching the low point is a rider 35 feet above the ground? You definitely need a picture for this one!

Explanation / Answer

angle of elevation to the top of 86th floor is 82 degrees

let x be the height from ground to the base of 86th floor

tan 82 = x + 123 / 45

x + 123 = tan 82 * 45

x + 123 = 320.19

x = 320.19 - 123

x = 197.19 metres

approximate height of building is 320.19 metres

b) applying cosine rule to find the distance between you and your friend

cos 82 = 45 / d

d = 45 / cos 82

d = 323.34 metres is distance bwteen you and your friend

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