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Elementary Geometry For College Students, 7e
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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### 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**: \( \cos C = \frac{11}{29} \)
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**: \( \cos C = \frac{11}{29} \)
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