/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 75 A tower that is 125 feet tall ca... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 75

A tower that is 125 feet tall casts a shadow 172 feet long. Find the angle of elevation of the Sun to the nearest degree.

Short Answer

Expert verified
The angle of elevation of the Sun is approximately 36 degrees.

Step by step solution

01

Identify Given Information

Based on the problem, the tower represents the opposite side with a length of 125 ft and the shadow represents the adjacent side with a length of 172 ft.
02

Apply the Tangent Formula

The formula for tangent is \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\). Plug in the values: \(\tan(\theta) = \frac{125}{172}\).
03

Solve for angle

Now, solve for \(\theta\) using the inverse tangent function. Therefore, \(\theta = \tan^{-1}(\frac{125}{172})\). The angle should be calculated in degrees.
04

Round to the Nearest Degree

Since the problem asks for the angle of elevation to the nearest degree, make sure to round the final answer.

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