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.
Solution
To find the angle of depression between the cliff and the boat, we can use the concept of trigonometry.
Given:
- The height of the cliff is 200 feet.
- The distance from the base of the cliff to the boat is 175 feet.
We can use the tangent function to find the angle of depression. The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Let’s denote the angle of depression as θ (theta).
Using the tangent function:
In this case, the opposite side is the height of the cliff (200 feet), and the adjacent side is the distance from the base of the cliff to the boat (175 feet).
Now, we can calculate the angle of depression by taking the inverse tangent (arctangent) of the ratio:
Let’s calculate the angle of depression.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Reduce the fraction:
The angle of depression between the cliff and the boat is approximately 0.851966 radians or 48.7 degrees.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
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!
