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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Question
![**Trigonometry Problem: Solving for x**
**Instructions:**
Using trigonometry, find angle \( x \). Round to the nearest tenth of a degree, if necessary.
**Diagram Explanation:**
The diagram depicts a right triangle labeled \( \triangle CDE \). The right angle is at point \( D \). The triangle has the following measurements:
- Side \( CD \) (adjacent to the angle \( x \)): 8 units
- Side \( CE \) (hypotenuse): 12 units
- The angle at \( E \) is unknown and labeled as \( x \).
**Steps to Solve the Problem:**
1. Identify the sides relative to the angle \( x \):
- Adjacent side: \( CD = 8 \)
- Hypotenuse: \( CE = 12 \)
2. Use the cosine function to find \( x \):
\[
\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{12}
\]
Simplifying the fraction:
\[
\cos(x) = \frac{2}{3}
\]
3. Find the angle \( x \) using the inverse cosine function:
\[
x = \cos^{-1}\left(\frac{2}{3}\right)
\]
4. Calculate \( x \) and round to the nearest tenth of a degree (using a calculator or a trigonometric table):
\[
x \approx 48.2^\circ
\]
**Final Answer:**
\( x \approx 48.2^\circ \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b09e42-7c9f-478b-83f0-998cebfd2878%2F40cc2d20-e949-40db-b8fb-589de860e77f%2Fvqlp6io_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Trigonometry Problem: Solving for x**
**Instructions:**
Using trigonometry, find angle \( x \). Round to the nearest tenth of a degree, if necessary.
**Diagram Explanation:**
The diagram depicts a right triangle labeled \( \triangle CDE \). The right angle is at point \( D \). The triangle has the following measurements:
- Side \( CD \) (adjacent to the angle \( x \)): 8 units
- Side \( CE \) (hypotenuse): 12 units
- The angle at \( E \) is unknown and labeled as \( x \).
**Steps to Solve the Problem:**
1. Identify the sides relative to the angle \( x \):
- Adjacent side: \( CD = 8 \)
- Hypotenuse: \( CE = 12 \)
2. Use the cosine function to find \( x \):
\[
\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{12}
\]
Simplifying the fraction:
\[
\cos(x) = \frac{2}{3}
\]
3. Find the angle \( x \) using the inverse cosine function:
\[
x = \cos^{-1}\left(\frac{2}{3}\right)
\]
4. Calculate \( x \) and round to the nearest tenth of a degree (using a calculator or a trigonometric table):
\[
x \approx 48.2^\circ
\]
**Final Answer:**
\( x \approx 48.2^\circ \)
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