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
![](/static/compass_v2/shared-icons/check-mark.png)
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
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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.Recommended textbooks for you
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning