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
![### Geometry Problem on Right Triangles
#### Problem Statement:
Find the length of the third side. If necessary, round to the nearest tenth.
#### Diagram Description:
The diagram depicts a right-angled triangle. One of the legs measures 12 units, and the hypotenuse measures 15 units. The length of the other leg needs to be calculated.
#### Solution:
To find the missing side length in a right-angled triangle, we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
Here:
- \( a \) is one leg of the triangle.
- \( b \) is the other leg of the triangle.
- \( c \) is the hypotenuse of the triangle.
Given:
- One leg \( a = 12 \)
- Hypotenuse \( c = 15 \)
We need to find the length of the other leg \( b \).
Using the Pythagorean theorem, we have:
\[
12^2 + b^2 = 15^2
\]
Calculating the squares:
\[
144 + b^2 = 225
\]
Solving for \( b^2 \):
\[
b^2 = 225 - 144 = 81
\]
Taking the square root of both sides:
\[
b = \sqrt{81} = 9
\]
Therefore, the length of the third side is:
\[
\boxed{9}
\]
#### User Interaction:
Enter the calculated length in the provided input box and click "Submit Answer" to verify your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef1017e2-941f-4fd9-b0bf-0c183073e70e%2F6b2b7ed6-295e-405c-ae76-1dc885f09e3d%2Frgk5e0a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem on Right Triangles
#### Problem Statement:
Find the length of the third side. If necessary, round to the nearest tenth.
#### Diagram Description:
The diagram depicts a right-angled triangle. One of the legs measures 12 units, and the hypotenuse measures 15 units. The length of the other leg needs to be calculated.
#### Solution:
To find the missing side length in a right-angled triangle, we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
Here:
- \( a \) is one leg of the triangle.
- \( b \) is the other leg of the triangle.
- \( c \) is the hypotenuse of the triangle.
Given:
- One leg \( a = 12 \)
- Hypotenuse \( c = 15 \)
We need to find the length of the other leg \( b \).
Using the Pythagorean theorem, we have:
\[
12^2 + b^2 = 15^2
\]
Calculating the squares:
\[
144 + b^2 = 225
\]
Solving for \( b^2 \):
\[
b^2 = 225 - 144 = 81
\]
Taking the square root of both sides:
\[
b = \sqrt{81} = 9
\]
Therefore, the length of the third side is:
\[
\boxed{9}
\]
#### User Interaction:
Enter the calculated length in the provided input box and click "Submit Answer" to verify your solution.
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