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
![### Find the Length of the Third Side
You are tasked with finding the length of the third side of a right triangle. If necessary, round your answer to the nearest tenth.
In the given right triangle, the lengths of two sides are provided:
- One leg of the triangle measures 24 units.
- The hypotenuse measures 25 units.
#### Diagram Explanation:
The diagram shows a right triangle with one right angle indicated. The lengths of the two sides are labeled:
- One leg (the side opposite the right angle) is labeled 24.
- The hypotenuse (the longest side opposite the right angle) is labeled 25.
Below the diagram, there is an input field labeled "Answer:" where you are expected to enter your calculated value. Additionally, there is a "Submit Answer" button to confirm your response.
This problem typically requires the application of the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the lengths of the legs of the triangle, and \( c \) is the length of the hypotenuse.
Given:
\[ a = 24 \]
\[ c = 25 \]
You need to find \( b \):
\[ 24^2 + b^2 = 25^2 \]
\[ 576 + b^2 = 625 \]
\[ b^2 = 625 - 576 \]
\[ b^2 = 49 \]
\[ b = \sqrt{49} \]
\[ b = 7 \]
Therefore, the length of the third side is **7 units**.
Input 7 in the answer field and click "Submit Answer" to check your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedac3c74-72d2-4f10-a845-e3e85ebfcd5c%2F076461f5-a0b6-4236-a91b-63ca2cf57cf7%2Fwufbq6.jpeg&w=3840&q=75)
Transcribed Image Text:### Find the Length of the Third Side
You are tasked with finding the length of the third side of a right triangle. If necessary, round your answer to the nearest tenth.
In the given right triangle, the lengths of two sides are provided:
- One leg of the triangle measures 24 units.
- The hypotenuse measures 25 units.
#### Diagram Explanation:
The diagram shows a right triangle with one right angle indicated. The lengths of the two sides are labeled:
- One leg (the side opposite the right angle) is labeled 24.
- The hypotenuse (the longest side opposite the right angle) is labeled 25.
Below the diagram, there is an input field labeled "Answer:" where you are expected to enter your calculated value. Additionally, there is a "Submit Answer" button to confirm your response.
This problem typically requires the application of the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the lengths of the legs of the triangle, and \( c \) is the length of the hypotenuse.
Given:
\[ a = 24 \]
\[ c = 25 \]
You need to find \( b \):
\[ 24^2 + b^2 = 25^2 \]
\[ 576 + b^2 = 625 \]
\[ b^2 = 625 - 576 \]
\[ b^2 = 49 \]
\[ b = \sqrt{49} \]
\[ b = 7 \]
Therefore, the length of the third side is **7 units**.
Input 7 in the answer field and click "Submit Answer" to check your solution.
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