Look at the triangle shown. What is the exact value of cos X? X Y 9. Note: Figure is not drawn to scale Your answer: V117 56.310 1.5 9. V117
Look at the triangle shown. What is the exact value of cos X? X Y 9. Note: Figure is not drawn to scale Your answer: V117 56.310 1.5 9. V117
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![**Triangle Cosine Calculation**
**Problem Statement:**
Look at the triangle shown. What is the exact value of cos X?
**Diagram Explanation:**
The triangle in the diagram is a right triangle XYZ with:
- Angle X as the angle we need to consider.
- Y being the right angle.
- The side opposite angle X (XY) is labeled as 6.
- The side adjacent to angle X (YZ) is labeled as 9.
- The hypotenuse (XZ) is labeled as the square root of 117 (√117).
- Note: Figure is not drawn to scale.
**Question:**
Your answer:
- ○ \(\frac{6}{\sqrt{117}}\)
- ○ 56.310
- ○ 1.5
- ○ \(\frac{9}{\sqrt{117}}\)
**Solution Explanation:**
To find the exact value of cos X, we use the definition of cosine for a right triangle, which is:
\[ \cos X = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]
Here, the adjacent side is YZ (which is 9) and the hypotenuse is XZ (which is √117). Therefore:
\[ \cos X = \frac{9}{\sqrt{117}} \]
So, the correct answer is:
- \(\frac{9}{\sqrt{117}}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bfa811e-5464-4643-8887-727be93de7c9%2Fef8d1344-c599-4462-8f88-14624caa154a%2Fr2xa9c_processed.png&w=3840&q=75)
Transcribed Image Text:**Triangle Cosine Calculation**
**Problem Statement:**
Look at the triangle shown. What is the exact value of cos X?
**Diagram Explanation:**
The triangle in the diagram is a right triangle XYZ with:
- Angle X as the angle we need to consider.
- Y being the right angle.
- The side opposite angle X (XY) is labeled as 6.
- The side adjacent to angle X (YZ) is labeled as 9.
- The hypotenuse (XZ) is labeled as the square root of 117 (√117).
- Note: Figure is not drawn to scale.
**Question:**
Your answer:
- ○ \(\frac{6}{\sqrt{117}}\)
- ○ 56.310
- ○ 1.5
- ○ \(\frac{9}{\sqrt{117}}\)
**Solution Explanation:**
To find the exact value of cos X, we use the definition of cosine for a right triangle, which is:
\[ \cos X = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]
Here, the adjacent side is YZ (which is 9) and the hypotenuse is XZ (which is √117). Therefore:
\[ \cos X = \frac{9}{\sqrt{117}} \]
So, the correct answer is:
- \(\frac{9}{\sqrt{117}}\)
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