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Chapter 4: Problem 60

A telephone pole is 55 feet tall. A guy wire 80 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the pole to the nearest degree.

Short Answer

Expert verified
The angle between the wire and the pole to the nearest degree is approximately 44 degrees.

Step by step solution

01

Identify the sides of the triangle

We have a right triangle where the pole is one side (opposite side), the wire is the hypotenuse, and we have to find the angle between the pole and the guy wire which we'll call 胃.
02

Use the sine function

The sine of an angle 胃 in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. So, sin(胃) will be equal to the length of the pole divided by the length of the guy wire which is: \( \sin(\theta) = \frac{55}{80} \).
03

Solve for 胃

To find 胃, we use the inverse sine function. So, 胃 will be equal to the inverse sine of the result from the previous step. Therefore, \( \theta = \arcsin\left(\frac{55}{80}\right) \). To find the angle to the nearest degree, use a calculator to evaluate the expression.

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