A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 25°. When the parasailer is attached to the boat with a 300-foot rope, how high above the boat is he? Round your answer to the nearest tenth of a
Question
A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 25°. When the parasailer is attached to the boat with a 300-foot rope, how high above the boat is he? Round your answer to the nearest tenth of a
Solution
To solve this problem, we can use the tangent of the angle of depression, which is the opposite side (height of the parasailer) over the adjacent side (distance along the ground).
The angle of depression is the same as the angle of elevation from the boat to the parasailer, which is 25°.
So, we have:
tan(25°) = height / 300 feet
To find the height, we rearrange the equation to solve for height:
height = tan(25°) * 300 feet
Using a calculator, tan(25°) is approximately 0.4663.
So, the height is approximately 0.4663 * 300 feet = 139.89 feet.
Rounding to the nearest tenth, the parasailer is approximately 139.9 feet above the boat.
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