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To solve the problem of finding the cosine of angle \( A \) in the right triangle \( ABC \), we use the definition of cosine:

\[
\cos(A) = \frac{\text{Adjacent}}{\text{Hypotenuse}}
\]

In this triangle:
- The side adjacent to angle \( A \) is \( 5 \) (side \( BC \)).
- The hypotenuse is \( 10 \) (side \( AB \)).

Thus, the cosine of angle \( A \) is:

\[
\cos(A) = \frac{5}{10} = \frac{1}{2}
\]

From the provided answer choices, the correct choice is:

\[
\boxed{\frac{5}{10}}
\]

Would you like further details on trigonometric ratios or have any other questions?

Here are 5 related questions to expand on this:
1. How is the sine of an angle defined in a right triangle?
2. What is the tangent of angle \( A \) in this triangle?
3. How do we calculate the length of the third side (side \( AC \)) using the Pythagorean theorem?
4. Can the cosine of angle \( A \) be negative in any situation? Why or why not?
5. How do trigonometric functions change for angles larger than 90 degrees?

**Tip:** In right triangles, the cosine of an acute angle is always positive and lies between 0 and 1.

In right triangle ABC above, what is the cosine of A?

Learn how to find the cosine of angle A in the right triangle ABC. This trigonometry problem covers key concepts like trigonometric ratios and the Pythagorean theorem, making it suitable for students in Grades 8-10.

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