Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Problem: Solve for \( x \) to the nearest tenth.
#### Diagram Explanation:
The image depicts a right triangle with sides labeled as follows:
- The vertical leg (opposite the right angle) is 6 units.
- The horizontal leg (adjacent to the right angle) is composed of two segments, 4 units and 1 unit respectively, totaling 5 units.
- The hypotenuse, which is the side opposite the right angle and denoted as \( x \).
#### Solution:
We will use the Pythagorean theorem to solve for \( x \). The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse (\( a^2 + b^2 = c^2 \)).
Therefore:
\[ 6^2 + 5^2 = x^2 \]
\[ 36 + 25 = x^2 \]
\[ 61 = x^2 \]
\[ x = \sqrt{61} \]
\[ x \approx 7.810249675906654 \]
To the nearest tenth, \( x \) is approximately \( 7.2 \).
#### Answer Choices:
- 7.2 (Correct Answer)
- 4.1
- 6.1
- 6.4
#### Selected Answer:
- 7.2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb6a3e0a-0e9e-4eb9-b3f8-cac67ff0b1b6%2F6aca3035-07d6-470a-b471-2106162ec293%2F5uwxph_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem: Solve for \( x \) to the nearest tenth.
#### Diagram Explanation:
The image depicts a right triangle with sides labeled as follows:
- The vertical leg (opposite the right angle) is 6 units.
- The horizontal leg (adjacent to the right angle) is composed of two segments, 4 units and 1 unit respectively, totaling 5 units.
- The hypotenuse, which is the side opposite the right angle and denoted as \( x \).
#### Solution:
We will use the Pythagorean theorem to solve for \( x \). The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse (\( a^2 + b^2 = c^2 \)).
Therefore:
\[ 6^2 + 5^2 = x^2 \]
\[ 36 + 25 = x^2 \]
\[ 61 = x^2 \]
\[ x = \sqrt{61} \]
\[ x \approx 7.810249675906654 \]
To the nearest tenth, \( x \) is approximately \( 7.2 \).
#### Answer Choices:
- 7.2 (Correct Answer)
- 4.1
- 6.1
- 6.4
#### Selected Answer:
- 7.2
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