Emir is standing in a treehouse and looking down at a swingset in the yard next door. The angle of depression from Emir's eyeline to the swingset is 33.69°, and Emir is 10 feet from the ground. How many feet is the base of the tree from the swingset? Round your answer to the nearest foot.

Question

Physics

Dominick Kennedy

8 September, 00:14

Emir is standing in a treehouse and looking down at a swingset in the yard next door. The angle of depression from Emir's eyeline to the swingset is 33.69°, and Emir is 10 feet from the ground. How many feet is the base of the tree from the swingset? Round your answer to the nearest foot.

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Answers (1)

Know the Answer?

Micah Sheppard · Answer 1

15 ft

Explanation:

We use tangent of angles. Let Ф = angle of depression of Emir's line of sight = angle of elevation of base of swingset from Emir = 33.69°. Let x = height of tree = 10 ft and y = distance of base of tree from swingset.

So tanФ = x/y and y = x/tanФ

y = x/tanФ

= 10 ft/tan33.69°

= 15 ft