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
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![### Right Triangle Problem
For any right triangle:
#### Directions:
Solve for \( x \). Round your answer to the nearest tenth.
#### Problem 1:
Consider a right triangle with one of the legs marked as \(9\) and the hypotenuse marked as \(17\). The other leg is denoted by \( x \).
The problem is presented with the following right triangle diagram:
- The right angle is marked at the corner between legs \(9\) and \( x \).
- The hypotenuse is marked as \(17\).
To solve for \( x \), use the Pythagorean theorem which states:
\[
a^2 + b^2 = c^2
\]
In this problem:
- \( a = 9 \)
- \( b = x \) (the unknown we are solving for)
- \( c = 17 \)
Thus, the equation becomes:
\[
9^2 + x^2 = 17^2
\]
Solve for \( x \):
\[
81 + x^2 = 289
\]
Subtract 81 from both sides:
\[
x^2 = 208
\]
Take the square root of both sides:
\[
x \approx 14.4
\]
Therefore, the length of \( x \) is approximately \( 14.4 \) units.
This exercise demonstrates the application of the Pythagorean theorem to solve for the length of a leg in a right triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa009fc37-cec7-4ab0-a64b-67649ce2067a%2F8bbd9552-f01d-4c0f-b06f-155b1f74c178%2Fv06u3wh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Right Triangle Problem
For any right triangle:
#### Directions:
Solve for \( x \). Round your answer to the nearest tenth.
#### Problem 1:
Consider a right triangle with one of the legs marked as \(9\) and the hypotenuse marked as \(17\). The other leg is denoted by \( x \).
The problem is presented with the following right triangle diagram:
- The right angle is marked at the corner between legs \(9\) and \( x \).
- The hypotenuse is marked as \(17\).
To solve for \( x \), use the Pythagorean theorem which states:
\[
a^2 + b^2 = c^2
\]
In this problem:
- \( a = 9 \)
- \( b = x \) (the unknown we are solving for)
- \( c = 17 \)
Thus, the equation becomes:
\[
9^2 + x^2 = 17^2
\]
Solve for \( x \):
\[
81 + x^2 = 289
\]
Subtract 81 from both sides:
\[
x^2 = 208
\]
Take the square root of both sides:
\[
x \approx 14.4
\]
Therefore, the length of \( x \) is approximately \( 14.4 \) units.
This exercise demonstrates the application of the Pythagorean theorem to solve for the length of a leg in a right triangle.
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