As Juliet stands 15 feet off the ground on her balcony, she spots Romeo in this distance, standing at the ground level. She uses her angle-measuring device and finds that his position is 3 degree from the horizontal (that is, the angle of depression is 3 degree.) To the nearest foot, how far away is Romeo from base of her balcony?

Question

Mathematics

Blake West

3 July, 17:29

As Juliet stands 15 feet off the ground on her balcony, she spots Romeo in this distance, standing at the ground level. She uses her angle-measuring device and finds that his position is 3 degree from the horizontal (that is, the angle of depression is 3 degree.) To the nearest foot, how far away is Romeo from base of her balcony?

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Answers (1)

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Pope · Answer 1

Let Romeo's distance from the base be x, then

tan 3° = 15/x

x = 15/tan 3° = 15/0.0524 = 286 feet

Therefore, Romeo is 286 feet from the base of the balcony.