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A man is in a boat that is floating 175 feet from the base of a 200-foot cliff. What is the angle of depression between the cliff and the boat?

Answer :

Final answer:

The angle of depression from the cliff to the boat is calculated by finding the inverse tangent of the ratio of the boat's distance to the cliff height, which equates to approximately 41.19°.

Explanation:

This problem can be solved using trigonometry. If we consider the cliff and the boat, we have a right triangle where the cliff is the adjacent side (200 feet), the boat is the opposite side (175 feet). To find the angle of depression, we have to use the tangent (tan) ratio which is opposite/adjacent. Tan(theta) = 175/200 = 0.875.

To find the angle, we need to use the inverse tangent function (also called atan or tan-1). Using a scientific calculator, we find that tan^-1 (0.875) is approximately 41.19°. However, this is the angle of elevation from the boat to the top of the cliff. The angle of depression from the cliff to the boat is the same as the angle of elevation due to alternate internal angles, so the angle of depression is also 41.19°.

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