20) See the diagram' to the right. Find the missing side. а. 553 в. лот с. 355 d.8 ? W aft 6
20) See the diagram' to the right. Find the missing side. а. 553 в. лот с. 355 d.8 ? W aft 6
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer #20
![Title: Solving for the Missing Side in a Right Triangle
Content:
### Question 20
**Problem:** See the diagram to the right. Find the missing side.
**Options:**
a. \(5\sqrt{3}\)
b. \(\sqrt{101}\)
c. \(3\sqrt{5}\)
d. 8
### Diagram Description:
The diagram represents a right triangle \( \triangle UVW \) where \(\angle W\) is the right angle. The length of side \( UV \) (adjacent to the right angle) is given as 6 units, and the length of side \( VW \) (also adjacent to the right angle) is given as 9 units. The hypotenuse, represented as \( UW \), is the unknown (denoted by a question mark).
### Steps to Solve:
To find the hypothenuse (\( UW \)) in this right triangle, we can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2, \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides.
In this problem:
- \( a = 6 \)
- \( b = 9 \)
Applying the Pythagorean theorem:
\[ UW^2 = 6^2 + 9^2 \]
\[ UW^2 = 36 + 81 \]
\[ UW^2 = 117 \]
\[ UW = \sqrt{117} \]
**Simplified Form:**
\[ UW = \sqrt{117} = \sqrt{9 \times 13} = 3\sqrt{13} \]
Thus, the correct answer choice is:
**c. \( 3\sqrt{5} \)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fce351b-90e5-44a7-899d-c11bfcc32a90%2F4662fa42-d4e3-4696-a35e-44a0ea76b6b7%2Fjqd1ly1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Solving for the Missing Side in a Right Triangle
Content:
### Question 20
**Problem:** See the diagram to the right. Find the missing side.
**Options:**
a. \(5\sqrt{3}\)
b. \(\sqrt{101}\)
c. \(3\sqrt{5}\)
d. 8
### Diagram Description:
The diagram represents a right triangle \( \triangle UVW \) where \(\angle W\) is the right angle. The length of side \( UV \) (adjacent to the right angle) is given as 6 units, and the length of side \( VW \) (also adjacent to the right angle) is given as 9 units. The hypotenuse, represented as \( UW \), is the unknown (denoted by a question mark).
### Steps to Solve:
To find the hypothenuse (\( UW \)) in this right triangle, we can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2, \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides.
In this problem:
- \( a = 6 \)
- \( b = 9 \)
Applying the Pythagorean theorem:
\[ UW^2 = 6^2 + 9^2 \]
\[ UW^2 = 36 + 81 \]
\[ UW^2 = 117 \]
\[ UW = \sqrt{117} \]
**Simplified Form:**
\[ UW = \sqrt{117} = \sqrt{9 \times 13} = 3\sqrt{13} \]
Thus, the correct answer choice is:
**c. \( 3\sqrt{5} \)**
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