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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掳.

Step by step solution

01

Identifying Given Values

From the problem, identify that the vertical height of the mountain (opposite) is 1500 feet, and the distance from the top to the bottom of the mountain (adjacent) is 3000 feet.
02

Apply the Tangent Function

Since we know the opposite and adjacent sides of a right-angled triangle and need to find an angle, we can use the tangent function, defined as Tan(theta) = Opposite/Adjacent. This translates into Tan(theta) = 1500/3000.
03

Solve for Angle

Now, take the inverse tangent of both sides to solve for theta, the unknown angle. Thus, theta = arctan(1500/3000). Eco sure to convert this calculation to degrees, if your calculator is set to radians.
04

Calculate the Angle

Perform the calculation theta = arctan(1500/3000) to find the angle of elevation from the base of the mountain to the top.

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