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
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Topic Video
Question
![### Understanding Right Triangles
**Diagram Explanation:**
The image contains a right triangle with one right angle indicated at the bottom left. The two known sides of the triangle are labeled as 9 (the base) and 15 (the hypotenuse or c side). The length of the other side is labeled as \( x \).
**Tasks:**
1. Identify the hypotenuse of the triangle.
2. Solve for \( x \).
**Questions:**
1. The hypotenuse or c side is: [Drop-down menu]
[Answer: 15]
2. Solve for \( x \):
\[ x = \; [Drop-down menu] \]
To solve for \( x \), use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
Given:
\[ a = 9 \]
\[ c = 15 \]
Calculate:
\[ x^2 + 9^2 = 15^2 \]
\[ x^2 + 81 = 225 \]
\[ x^2 = 225 - 81 \]
\[ x^2 = 144 \]
\[ x = \sqrt{144} \]
\[ x = 12 \]
Therefore:
\[ x = 12 \]
**Final Answer:**
\[ x = 12 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab545a03-1d39-4874-800c-bed9ffa7318e%2F6c491210-3b56-467a-b9d7-52ef9bfaf39b%2F1g55bb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Right Triangles
**Diagram Explanation:**
The image contains a right triangle with one right angle indicated at the bottom left. The two known sides of the triangle are labeled as 9 (the base) and 15 (the hypotenuse or c side). The length of the other side is labeled as \( x \).
**Tasks:**
1. Identify the hypotenuse of the triangle.
2. Solve for \( x \).
**Questions:**
1. The hypotenuse or c side is: [Drop-down menu]
[Answer: 15]
2. Solve for \( x \):
\[ x = \; [Drop-down menu] \]
To solve for \( x \), use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
Given:
\[ a = 9 \]
\[ c = 15 \]
Calculate:
\[ x^2 + 9^2 = 15^2 \]
\[ x^2 + 81 = 225 \]
\[ x^2 = 225 - 81 \]
\[ x^2 = 144 \]
\[ x = \sqrt{144} \]
\[ x = 12 \]
Therefore:
\[ x = 12 \]
**Final Answer:**
\[ x = 12 \]
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