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Chapter 10: Problem 44

The Washington Monument is 555 feet high. If you stand one quarter of a mile, or 1320 feet, from the base of the monument and look to the top, find the angle of elevation to the nearest degree.

Short Answer

Expert verified
The angle of elevation to the nearest degree

Step by step solution

01

Understand the Problem

First, identify where to use trigonometry. There is a right triangle formed by the height of the monument, the distance of the observer from the base, and the line of sight from the observer to the top. The angle of elevation is the angle from the observer's line of sight to the horizon. Here, the problem provides the distances of the other two sides, 'opposite' and 'adjacent'.
02

Find The Ratio of The Two Sides

Next, calculate the ratio of the 'opposite' side, which is the height of the monument, to the 'adjacent' side, which is the distance from the observer to the base of the monument. That is, calculate \( \frac{555}{1320} \).
03

Calculate Degree

Calculating the inverse tangent of the fraction will give the answer in radians. We need to convert it to degrees since the problem asks for the answer in degrees. To convert from radians to degrees, multiply by \( \frac{180}{\pi} \). So, the degree is \( \alpha = \theta \times \frac{180}{\pi} \). Calculate it using a calculator.

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