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
![**Solve for \( x \) in the triangle. Round your answer to the nearest tenth.**
The image shows a right triangle with one non-right angle labeled as \( 25^\circ \). The side opposite the right angle, or hypotenuse, is labeled as \( x \). The side adjacent to the \( 25^\circ \) angle is labeled as \( 8 \).
To solve for \( x \), use the cosine function, which relates the adjacent side and the hypotenuse in a right triangle:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case:
\[ \cos(25^\circ) = \frac{8}{x} \]
To solve for \( x \), rearrange the equation:
\[ x = \frac{8}{\cos(25^\circ)} \]
Use a calculator to evaluate:
\[ \cos(25^\circ) \approx 0.9063 \]
Then:
\[ x = \frac{8}{0.9063} \approx 8.8 \]
Therefore, the length of the hypotenuse \( x \) is approximately \( 8.8 \) units, rounded to the nearest tenth. Enter the value into the provided text box:
\[ x = \boxed{8.8} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd1ff857-92ff-4e51-81f6-c8581968700f%2F91ced3a2-316f-4429-adad-300b883df168%2Flnnzlj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for \( x \) in the triangle. Round your answer to the nearest tenth.**
The image shows a right triangle with one non-right angle labeled as \( 25^\circ \). The side opposite the right angle, or hypotenuse, is labeled as \( x \). The side adjacent to the \( 25^\circ \) angle is labeled as \( 8 \).
To solve for \( x \), use the cosine function, which relates the adjacent side and the hypotenuse in a right triangle:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case:
\[ \cos(25^\circ) = \frac{8}{x} \]
To solve for \( x \), rearrange the equation:
\[ x = \frac{8}{\cos(25^\circ)} \]
Use a calculator to evaluate:
\[ \cos(25^\circ) \approx 0.9063 \]
Then:
\[ x = \frac{8}{0.9063} \approx 8.8 \]
Therefore, the length of the hypotenuse \( x \) is approximately \( 8.8 \) units, rounded to the nearest tenth. Enter the value into the provided text box:
\[ x = \boxed{8.8} \]
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