https://file.aiquickdraw.com/mathbot/file/17268032998757jly0c9z.jpg

To find the cosine of the angle \(\theta\), we use the definition of cosine in a right triangle:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

From the diagram:

- The adjacent side to angle \(\theta\) is 12.
- The hypotenuse is 13.

Thus,

\[
\cos(\theta) = \frac{12}{13}
\]

This is the exact value of \(\cos(\theta)\).

Would you like further details or explanations? Here are some related questions for deeper understanding:

1. How is the cosine function used in other types of triangles?
2. What are the sine and tangent of angle \(\theta\) in this triangle?
3. How do we confirm this triangle is a right triangle using the Pythagorean theorem?
4. Can we find the angle \(\theta\) using an inverse trigonometric function?
5. How would we calculate \(\sin(2\theta)\) using the double-angle formula?

**Tip**: The cosine of an angle in a right triangle is always the ratio of the length of the adjacent side to the hypotenuse.

Find cos(θ), where θ is the angle shown in the right triangle with sides 13 (hypotenuse), 12 (adjacent), and unknown opposite side. Give an exact value, not a decimal approximation.

Learn how to find the exact value of cos(θ) in a right triangle where the adjacent side is 12 and the hypotenuse is 13. This trigonometry problem covers key concepts like cosine ratios and the Pythagorean theorem. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation