A telephone pole, shown at the top of the next column, is 60 feet tall. A guy wire 78 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. 60 ft 78 ft The angle between the wire and the pole is approximately degrees. (Round to the nearest degree.)
A telephone pole, shown at the top of the next column, is 60 feet tall. A guy wire 78 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. 60 ft 78 ft The angle between the wire and the pole is approximately degrees. (Round to the nearest degree.)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![### Determining the Angle Between a Wire and a Pole
#### Problem Statement:
A telephone pole, shown at the top of the next column, is 60 feet tall. A guy wire 78 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.
##### Diagram Explanation:
- The diagram depicts a right triangle standing on the ground.
- The vertical leg of the triangle represents the telephone pole, which is 60 feet tall.
- The hypotenuse of the triangle represents the guy wire, which is 78 feet long.
- The horizontal leg of the triangle, which is the distance on the ground between the base of the pole and the point where the wire is anchored, is not given directly but can be calculated using the Pythagorean theorem.
#### Calculation:
The angle between the wire and the pole can be calculated using trigonometry. Specifically, the sine function relates the opposite side (height of the pole) to the hypotenuse (length of the wire):
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{60}{78}
\]
To find the angle \( \theta \):
\[
\theta = \sin^{-1}\left( \frac{60}{78} \right)
\]
#### Final Answer:
The angle between the wire and the pole is approximately
\[
\boxed{\text{[Enter calculated angle here]}} \text{ degrees}
\]
(Round to the nearest degree)
##### Enter your answer in the answer box below.
---
For more information on trigonometric functions and how they can be used to solve problems involving right triangles, please visit our [Education Section on Trigonometry](#).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad727bdc-baba-4947-a2e3-e934fc451c32%2F9e463352-e5ce-4a9c-a2f8-3e7724fdedbb%2Ftu0a35_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Angle Between a Wire and a Pole
#### Problem Statement:
A telephone pole, shown at the top of the next column, is 60 feet tall. A guy wire 78 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.
##### Diagram Explanation:
- The diagram depicts a right triangle standing on the ground.
- The vertical leg of the triangle represents the telephone pole, which is 60 feet tall.
- The hypotenuse of the triangle represents the guy wire, which is 78 feet long.
- The horizontal leg of the triangle, which is the distance on the ground between the base of the pole and the point where the wire is anchored, is not given directly but can be calculated using the Pythagorean theorem.
#### Calculation:
The angle between the wire and the pole can be calculated using trigonometry. Specifically, the sine function relates the opposite side (height of the pole) to the hypotenuse (length of the wire):
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{60}{78}
\]
To find the angle \( \theta \):
\[
\theta = \sin^{-1}\left( \frac{60}{78} \right)
\]
#### Final Answer:
The angle between the wire and the pole is approximately
\[
\boxed{\text{[Enter calculated angle here]}} \text{ degrees}
\]
(Round to the nearest degree)
##### Enter your answer in the answer box below.
---
For more information on trigonometric functions and how they can be used to solve problems involving right triangles, please visit our [Education Section on Trigonometry](#).
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