Monica is standing on top of a building looking down at her friend, who is standing in a nearby park. The angle of depression (of her gaze) is at 36 degrees. If the building that Monica is standing on is 123 ft. tall, then what is the distance between Monica and her friend? Write your answer to the nearest foot.
Question
Monica is standing on top of a building looking down at her friend, who is standing in a nearby park. The angle of depression (of her gaze) is at 36 degrees. If the building that Monica is standing on is 123 ft. tall, then what is the distance between Monica and her friend? Write your answer to the nearest foot.
Solution
To solve this problem, we can use the tangent of the angle of depression, which is the ratio of the opposite side (the height of the building) to the adjacent side (the distance from the base of the building to Monica's friend).
The formula for tangent is tan(θ) = opposite/adjacent.
We know the angle of depression (θ) is 36 degrees and the height of the building (opposite) is 123 ft. We want to find the distance from the base of the building to Monica's friend (adjacent).
Rearranging the formula to solve for the adjacent side gives us: adjacent = opposite/tan(θ).
Substituting the given values into the formula gives us: adjacent = 123/tan(36).
Using a calculator to find the tangent of 36 degrees and then divide 123 by that number gives us the distance from the base of the building to Monica's friend, which is approximately 174 feet.
So, the distance between Monica and her friend is about 174 feet.
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