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To solve for \(\sin A\), \(\tan A\), and \(\cos A\) in the given right triangle, we use the basic trigonometric definitions:

### Given:
- The triangle is a right triangle with sides 3, 4, and 5.
- Hypotenuse (\(BC\)) = 5
- Opposite side to angle \(A\) (\(AB\)) = 3
- Adjacent side to angle \(A\) (\(AC\)) = 4

### Trigonometric definitions:
1. **\(\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AB}{BC} = \frac{3}{5} = 0.6\)**
2. **\(\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{AC}{BC} = \frac{4}{5} = 0.8\)**
3. **\(\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{AB}{AC} = \frac{3}{4} = 0.75\)**

Thus:
- \(\sin A = 0.6\)
- \(\cos A = 0.8\)
- \(\tan A = 0.75\)

Would you like a more detailed explanation, or do you have any further questions? Here are some related questions to further your understanding:

1. What are the definitions of \(\sin B\), \(\cos B\), and \(\tan B\) for this triangle?
2. How would the trigonometric ratios change if we used angle \(B\) instead of angle \(A\)?
3. What is the Pythagorean Theorem and how is it applied to this triangle?
4. How can we use trigonometric identities to verify the results?
5. Can you find the values of \(\cot A\), \(\sec A\), and \(\csc A\)?

**Tip:** In any right triangle, \(\sin A\) and \(\cos A\) are related by the Pythagorean identity: \(\sin^2 A + \cos^2 A = 1\).

A right triangle has side lengths 3, 4, and 5. Use these lengths to find sin A, tan A, and cos A.

Learn how to calculate sin A, tan A, and cos A for a right triangle with side lengths 3, 4, and 5. This example covers basic trigonometric ratios, including sine, cosine, and tangent, along with the Pythagorean Theorem. Suitable for students in Grades 8-10.

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