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
![## Solving for an Angle in a Right Triangle
### Problem Statement
**Solve for \( x \). Round to the nearest tenth of a degree, if necessary.**
### Given Diagram
The diagram shows a right triangle \( \triangle CDE \) where ∠DCE is a right angle. The sides of the triangle are labeled as follows:
- Side \( CD \) (adjacent to \( x^\circ \)): 2.1
- Side \( CE \) (the hypotenuse): 4
The angle \( x^\circ \) is at vertex \( E \), opposite side \( CD \).
### Steps to Solve
1. **Identify known values**:
- Adjacent side \( CD \) = 2.1
- Hypotenuse \( CE \) = 4
- Use the cosine function \( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \).
2. **Calculate \( x^\circ \)**:
Use the cosine function:
\[
\cos x^\circ = \frac{2.1}{4}
\]
Calculate the value of \(\frac{2.1}{4}\):
\[
\cos x^\circ = 0.525
\]
Next, use the inverse cosine (arccos) function to find \( x \):
\[
x = \cos^{-1}(0.525) \approx 58.4^\circ
\]
3. **Conclusion**:
The value of the angle \( x \) is approximately \( 58.4^\circ \).
### Input
You are required to enter the value of \( x \) in the textbox and click "Submit Answer" to check your solution.
**Answer: \( x = \) ____°**
Please enter your calculated value for \( x \) rounded to the nearest tenth of a degree.
### Visualization - Detailed Description of Diagram
- A right-angled triangle \( CDE \).
- \(\angle DCE\) is a right angle.
- Side \( CD \) is 2.1 units long, adjacent to \( x^\circ \).
- Side \( CE \) is the hypotenuse, 4 units long.
- \(\angle DEC\) is marked as \( x^\circ \).
Ensure to round to the nearest tenth as](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9a9c957-5085-44f4-ae3b-11d5320b66b1%2F2c89a955-a413-4a00-83be-5ea1d01adf9b%2Fgkqz18a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Solving for an Angle in a Right Triangle
### Problem Statement
**Solve for \( x \). Round to the nearest tenth of a degree, if necessary.**
### Given Diagram
The diagram shows a right triangle \( \triangle CDE \) where ∠DCE is a right angle. The sides of the triangle are labeled as follows:
- Side \( CD \) (adjacent to \( x^\circ \)): 2.1
- Side \( CE \) (the hypotenuse): 4
The angle \( x^\circ \) is at vertex \( E \), opposite side \( CD \).
### Steps to Solve
1. **Identify known values**:
- Adjacent side \( CD \) = 2.1
- Hypotenuse \( CE \) = 4
- Use the cosine function \( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \).
2. **Calculate \( x^\circ \)**:
Use the cosine function:
\[
\cos x^\circ = \frac{2.1}{4}
\]
Calculate the value of \(\frac{2.1}{4}\):
\[
\cos x^\circ = 0.525
\]
Next, use the inverse cosine (arccos) function to find \( x \):
\[
x = \cos^{-1}(0.525) \approx 58.4^\circ
\]
3. **Conclusion**:
The value of the angle \( x \) is approximately \( 58.4^\circ \).
### Input
You are required to enter the value of \( x \) in the textbox and click "Submit Answer" to check your solution.
**Answer: \( x = \) ____°**
Please enter your calculated value for \( x \) rounded to the nearest tenth of a degree.
### Visualization - Detailed Description of Diagram
- A right-angled triangle \( CDE \).
- \(\angle DCE\) is a right angle.
- Side \( CD \) is 2.1 units long, adjacent to \( x^\circ \).
- Side \( CE \) is the hypotenuse, 4 units long.
- \(\angle DEC\) is marked as \( x^\circ \).
Ensure to round to the nearest tenth as
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