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
![### Pythagorean Theorem Example Problem
#### Problem:
Find the length of the third side. If necessary, round to the nearest tenth.
#### Solution:
In this problem, you are tasked with finding the length of the third side of a right-angled triangle. The triangle is illustrated with one right angle, making it ideal for the application of the Pythagorean Theorem.
The Pythagorean Theorem states:
\[ a^2 + b^2 = c^2 \]
where \( c \) represents the hypotenuse (the side opposite the right angle), and \( a \) and \( b \) represent the other two sides.
In the given triangle:
- One leg \(a\) = 12 units
- Hypotenuse \(c\) = 15 units
We need to find the length of the other leg \(b\).
By substituting the known values into the Pythagorean Theorem:
\[ 12^2 + b^2 = 15^2 \]
\[ 144 + b^2 = 225 \]
Solving for \( b^2 \):
\[ b^2 = 225 - 144 \]
\[ b^2 = 81 \]
To find \( b \), we take the square root of 81:
\[ b = \sqrt{81} \]
\[ b = 9 \]
Therefore, the length of the third side is 9 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1ee66a4-8e77-4cb9-b1b9-9bd40d747386%2F7fe01ac2-b933-47f6-9eb5-7679b06c56e3%2Fwc8ubi6_processed.png&w=3840&q=75)
Transcribed Image Text:### Pythagorean Theorem Example Problem
#### Problem:
Find the length of the third side. If necessary, round to the nearest tenth.
#### Solution:
In this problem, you are tasked with finding the length of the third side of a right-angled triangle. The triangle is illustrated with one right angle, making it ideal for the application of the Pythagorean Theorem.
The Pythagorean Theorem states:
\[ a^2 + b^2 = c^2 \]
where \( c \) represents the hypotenuse (the side opposite the right angle), and \( a \) and \( b \) represent the other two sides.
In the given triangle:
- One leg \(a\) = 12 units
- Hypotenuse \(c\) = 15 units
We need to find the length of the other leg \(b\).
By substituting the known values into the Pythagorean Theorem:
\[ 12^2 + b^2 = 15^2 \]
\[ 144 + b^2 = 225 \]
Solving for \( b^2 \):
\[ b^2 = 225 - 144 \]
\[ b^2 = 81 \]
To find \( b \), we take the square root of 81:
\[ b = \sqrt{81} \]
\[ b = 9 \]
Therefore, the length of the third side is 9 units.
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