Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.2: Indirect Proof
Problem 23E: A periscope uses an indirect method of observation. This instrument allows one to see what would...
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5. Use the diagram to find the value of x and to find the degree of angle A.
![### Geometry Problem: Solving for Triangle Side Length
#### Question 5/36
**Use the following diagram to solve for each measurement:**
**(a)**
A right triangle is depicted with vertices labeled A, B, and C. The right angle is at vertex C. The length of side AC is labeled as \(x\), the length of side BC is labeled as 5, and the length of the hypotenuse AB is labeled as 14.
**Given Values:**
- Hypotenuse (AB) = 14
- Side BC = 5
**Diagram Explanation:**
- Triangle ABC is a right triangle.
- \(AB\) is the hypotenuse.
- \(BC\) is one of the legs adjoining the right angle.
- \(AC\) is the other leg adjoining the right angle and is labeled as \(x\).
**Objective:**
Find the length of side \(x\) using the Pythagorean Theorem.
\[
\text{Pythagorean Theorem}: \, a^2 + b^2 = c^2
\]
Where:
- \(a\) and \(b\) are the legs of the right triangle.
- \(c\) is the hypotenuse.
**Calculation:**
1. Assign values:
\[
x^2 + 5^2 = 14^2
\]
2. Solve for \(x\):
\[
x^2 + 25 = 196
\]
\[
x^2 = 196 - 25
\]
\[
x^2 = 171
\]
3. Taking the square root of both sides:
\[
x = \sqrt{171}
\]
**Answer Options:**
A. \(171\)
B. \(221\)
C. \(3 \sqrt{19}\)
D. \(- \sqrt{221}\)
**Correct Answer:**
The correct answer for \(x\) is:
C. \( \sqrt{171} = 3\sqrt{19} \)
This calculation concludes with confirming the correct option from the given list.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34bff1e1-af68-4229-b0ef-aa0aaa134e46%2Fa666a034-f760-4a5c-b900-c242cd2c2d8b%2Fswp6dxa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Solving for Triangle Side Length
#### Question 5/36
**Use the following diagram to solve for each measurement:**
**(a)**
A right triangle is depicted with vertices labeled A, B, and C. The right angle is at vertex C. The length of side AC is labeled as \(x\), the length of side BC is labeled as 5, and the length of the hypotenuse AB is labeled as 14.
**Given Values:**
- Hypotenuse (AB) = 14
- Side BC = 5
**Diagram Explanation:**
- Triangle ABC is a right triangle.
- \(AB\) is the hypotenuse.
- \(BC\) is one of the legs adjoining the right angle.
- \(AC\) is the other leg adjoining the right angle and is labeled as \(x\).
**Objective:**
Find the length of side \(x\) using the Pythagorean Theorem.
\[
\text{Pythagorean Theorem}: \, a^2 + b^2 = c^2
\]
Where:
- \(a\) and \(b\) are the legs of the right triangle.
- \(c\) is the hypotenuse.
**Calculation:**
1. Assign values:
\[
x^2 + 5^2 = 14^2
\]
2. Solve for \(x\):
\[
x^2 + 25 = 196
\]
\[
x^2 = 196 - 25
\]
\[
x^2 = 171
\]
3. Taking the square root of both sides:
\[
x = \sqrt{171}
\]
**Answer Options:**
A. \(171\)
B. \(221\)
C. \(3 \sqrt{19}\)
D. \(- \sqrt{221}\)
**Correct Answer:**
The correct answer for \(x\) is:
C. \( \sqrt{171} = 3\sqrt{19} \)
This calculation concludes with confirming the correct option from the given list.
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