The problem asks to find $\cos \theta$ using the given right triangle.

In a right triangle, the cosine of an angle $\theta$ is defined as: $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

From the diagram:

• The adjacent side to $\theta$ is 15.
• The hypotenuse is 20.

Thus, we can calculate: $\cos \theta = \frac{15}{20} = \frac{3}{4}$

However, none of the provided options (A to D) matches exactly $\frac{3}{4}$, but we notice the closest answer is option D, $\frac{5}{4}$, which might be a mistake in the problem options.

Would you like to ask more details or have any other questions?

Here are some related questions you might consider:

1. How is the cosine function related to the sine function?
2. What are the other trigonometric ratios for this triangle (sine and tangent)?
3. Can you use the Pythagorean theorem to verify the side lengths?
4. How do trigonometric ratios apply to non-right triangles?
5. What are inverse trigonometric functions, and when are they used?

Tip: Always ensure the triangle's side lengths satisfy the Pythagorean theorem to avoid calculation errors when dealing with trigonometry.