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Chapter 4: Problem 69

You are skiing down a mountain with a vertical height of 1500 feet. The distance from the top of the mountain to the base is 3000 feet. What is the angle of elevation from the base to the top of the mountain?

Short Answer

Expert verified
The angle of elevation from the base to the top of the mountain is approximately 26.57 degrees.

Step by step solution

01

- Define Variables

Let's denote the angle of elevation as \(\theta\). The 'opposite' in the context of our problem is the vertical height of the mountain, which is 1500 feet. The 'adjacent' refers to the distance from the base to the top of the mountain, that is, 3000 feet.
02

- Apply Trigonometric Ratio Formula

Using the formula for the tangent of an angle, we can write the equation as follows: \(\tan(\theta) = \frac{1500}{3000}\).
03

- Solve for Theta

Solving the above equation will give us the value of \(\tan(\theta)\). To find \(\theta\), we need to apply the inverse tangent function (also known as arctan) to both sides. This gives \(\theta = \arctan(\frac{1500}{3000})\).
04

- Compute the Angle of Elevation

Using a calculator, we find that \(\theta \approx 26.57\) degrees.

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