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 presents a right-angled triangle with one side labeled \( 10 \), one angle labeled \( 40^\circ \), and the hypotenuse labeled \( x \).
- **Triangle Diagram:**
- The angle at the base of the triangle is \( 40^\circ \).
- The side opposite the \( 40^\circ \) angle is the hypotenuse, labeled \( x \).
- The side adjacent to the \( 40^\circ \) angle is labeled \( 10 \).
- The right angle is at the lower left corner of the triangle.
The problem asks you to solve for \( x \), the hypotenuse, and round your answer to the nearest tenth.
**Solution Box:**
\[
x = \boxed{}
\]
**Icons:**
- An "X" icon likely to cancel the answer.
- A "reset" icon to clear the entered value.
- A question mark icon for help.
To solve for \( x \):
1. Use the cosine function: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
2. Here, \(\theta = 40^\circ\), \(\text{adjacent} = 10\), and \(\text{hypotenuse} = x\).
3. \(\cos(40^\circ) = \frac{10}{x}\)
4. Rearrange to solve for \( x \):
\[
x = \frac{10}{\cos(40^\circ)}
\]
5. Calculate using a calculator:
\[
\cos(40^\circ) \approx 0.766
\]
\[
x \approx \frac{10}{0.766} \approx 13.1
\]
So, the value of \( x \) rounded to the nearest tenth is \( 13.1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd1ff857-92ff-4e51-81f6-c8581968700f%2Fe24b2d92-0872-4022-a889-0e313a92b526%2Feiynsiq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for \( x \) in the triangle. Round your answer to the nearest tenth.**
The image presents a right-angled triangle with one side labeled \( 10 \), one angle labeled \( 40^\circ \), and the hypotenuse labeled \( x \).
- **Triangle Diagram:**
- The angle at the base of the triangle is \( 40^\circ \).
- The side opposite the \( 40^\circ \) angle is the hypotenuse, labeled \( x \).
- The side adjacent to the \( 40^\circ \) angle is labeled \( 10 \).
- The right angle is at the lower left corner of the triangle.
The problem asks you to solve for \( x \), the hypotenuse, and round your answer to the nearest tenth.
**Solution Box:**
\[
x = \boxed{}
\]
**Icons:**
- An "X" icon likely to cancel the answer.
- A "reset" icon to clear the entered value.
- A question mark icon for help.
To solve for \( x \):
1. Use the cosine function: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
2. Here, \(\theta = 40^\circ\), \(\text{adjacent} = 10\), and \(\text{hypotenuse} = x\).
3. \(\cos(40^\circ) = \frac{10}{x}\)
4. Rearrange to solve for \( x \):
\[
x = \frac{10}{\cos(40^\circ)}
\]
5. Calculate using a calculator:
\[
\cos(40^\circ) \approx 0.766
\]
\[
x \approx \frac{10}{0.766} \approx 13.1
\]
So, the value of \( x \) rounded to the nearest tenth is \( 13.1 \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning