Question
- 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?
is
the angle of depression between the cliff and the boat?
Ask by Pollard Medina. in the United States
Jan 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The angle of depression between the cliff and the boat is approximately 48.7 degrees.
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To find the angle of depression, you can visualize the scenario as a right triangle where the height of the cliff (200 feet) is the opposite side and the distance from the base of the cliff to the boat (175 feet) is the adjacent side. You can use the tangent function:
tan(θ) = opposite/adjacent = 200/175.
Calculating the angle, θ = arctan(200/175). Using a calculator, you will find that θ is approximately 48.37 degrees. So, the angle of depression from the top of the cliff to the boat is about 48.37 degrees!
And remember, whether you’re floating on water or just reading this, angles always come to play!