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
instructions in photo
![### Express cos C as a fraction in simplest terms.
In the given figure, we have a right triangle \( \triangle CDE \) with:
- \( DE \) as the hypotenuse of length 29 units
- \( CD \) as one of the legs of length 11 units
- \( \angle DCE \) being the right angle (90 degrees)
To express \( \cos C \) as a fraction in simplest terms, we use the definition of cosine in a right triangle:
\[ \cos C = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]
Here, the adjacent side to \( \angle C \) is \( CD \), which has a length of 11 units, and the hypotenuse is \( DE \), which has a length of 29 units.
Thus,
\[ \cos C = \frac{CD}{DE} = \frac{11}{29} \]
This fraction is already in its simplest terms.
### Summary
- **Right Triangle** \( \triangle CDE \)
- **Lengths**: \( CD = 11 \), \( DE = 29 \)
- **Cosine**: \( \cos C = \frac{11}{29} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddc6b782-5568-4e4b-a41c-c5410dd3aea4%2F8f3e0685-8b5a-46b8-b90e-763205ccab83%2Fhfv8hrl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Express cos C as a fraction in simplest terms.
In the given figure, we have a right triangle \( \triangle CDE \) with:
- \( DE \) as the hypotenuse of length 29 units
- \( CD \) as one of the legs of length 11 units
- \( \angle DCE \) being the right angle (90 degrees)
To express \( \cos C \) as a fraction in simplest terms, we use the definition of cosine in a right triangle:
\[ \cos C = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]
Here, the adjacent side to \( \angle C \) is \( CD \), which has a length of 11 units, and the hypotenuse is \( DE \), which has a length of 29 units.
Thus,
\[ \cos C = \frac{CD}{DE} = \frac{11}{29} \]
This fraction is already in its simplest terms.
### Summary
- **Right Triangle** \( \triangle CDE \)
- **Lengths**: \( CD = 11 \), \( DE = 29 \)
- **Cosine**: \( \cos C = \frac{11}{29} \)
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 with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Similar questions
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