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In the right triangle \(ABC\), we need to find the sine of angle \(A\).

In a right triangle, the sine of an angle is defined as:

\[
\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}
\]

Here, for \(\angle A\):

- The side opposite to \(\angle A\) is \(6\) (side \(AC\)).
- The hypotenuse is \(7\) (side \(AB\)).

So, the sine of \(\angle A\) is:

\[
\sin(A) = \frac{6}{7}
\]

Thus, the correct answer is:

\[
\boxed{\frac{6}{7}}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. How do you find the cosine of \(\angle A\) in a right triangle?
2. What is the tangent of \(\angle A\) in this triangle?
3. How can you determine \(\sin(B)\) from the given information?
4. How does the Pythagorean theorem apply to this triangle?
5. What is the relationship between sine and cosine for complementary angles?

**Tip:** Remember that in a right triangle, the sine and cosine of complementary angles (like \(\angle A\) and \(\angle B\)) are related: \(\sin(A) = \cos(B)\) and vice versa.

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

Learn how to find the sine of angle A in a right triangle using the formula sin(θ) = opposite / hypotenuse. In this problem, the side opposite to angle A is 6, and the hypotenuse is 7, making sin(A) = 6/7. Suitable for students in Grades 7-9.

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