Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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![### Problem 20: Bracing a Telephone Pole
**Problem Statement:**
A 26-foot-tall telephone pole will be braced with a wire that extends from the top of the pole to a point 18 feet from the base of the pole. How long will the wire need to be? Provide the answer to the nearest tenth of a foot.
**Visual Representation:**
The problem includes a right triangle diagram, where:
- The vertical side represents the height of the telephone pole, measuring 26 feet.
- The horizontal side represents the distance from the base of the pole to the point where the wire attaches to the ground, measuring 18 feet.
**Diagram Explanation:**
The right triangle diagram demonstrates a right-angle triangle with the following annotated sides:
- The vertical side (opposite) is labeled 26 feet.
- The horizontal side (adjacent) is labeled 18 feet.
- The hypotenuse, which represents the length of the wire, is not labeled but is what needs to be calculated.
**Solution:**
To determine the length of the wire (the hypotenuse), we use the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
Where:
- \( a \) is the height of the pole (26 feet)
- \( b \) is the distance from the base of the pole (18 feet)
- \( c \) is the length of the wire
Calculating:
\[ c = \sqrt{26^2 + 18^2} \]
\[ c = \sqrt{676 + 324} \]
\[ c = \sqrt{1000} \]
\[ c \approx 31.6 \text{ feet} \]
**Answer:**
The wire will need to be approximately 31.6 feet long.](https://content.bartleby.com/qna-images/question/8918ac98-5bcf-465f-8c11-409b4d478a84/0456f5be-5285-42b0-8261-2360d50e8b4f/0j9loga.jpeg)
Transcribed Image Text:### Problem 20: Bracing a Telephone Pole
**Problem Statement:**
A 26-foot-tall telephone pole will be braced with a wire that extends from the top of the pole to a point 18 feet from the base of the pole. How long will the wire need to be? Provide the answer to the nearest tenth of a foot.
**Visual Representation:**
The problem includes a right triangle diagram, where:
- The vertical side represents the height of the telephone pole, measuring 26 feet.
- The horizontal side represents the distance from the base of the pole to the point where the wire attaches to the ground, measuring 18 feet.
**Diagram Explanation:**
The right triangle diagram demonstrates a right-angle triangle with the following annotated sides:
- The vertical side (opposite) is labeled 26 feet.
- The horizontal side (adjacent) is labeled 18 feet.
- The hypotenuse, which represents the length of the wire, is not labeled but is what needs to be calculated.
**Solution:**
To determine the length of the wire (the hypotenuse), we use the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
Where:
- \( a \) is the height of the pole (26 feet)
- \( b \) is the distance from the base of the pole (18 feet)
- \( c \) is the length of the wire
Calculating:
\[ c = \sqrt{26^2 + 18^2} \]
\[ c = \sqrt{676 + 324} \]
\[ c = \sqrt{1000} \]
\[ c \approx 31.6 \text{ feet} \]
**Answer:**
The wire will need to be approximately 31.6 feet long.
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