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To find the trigonometric ratios for the given right triangles, we will calculate the sine, cosine, and tangent for each angle.

### Triangle a:
- The triangle has sides 5 (opposite to angle \( \alpha \)), 12 (adjacent to angle \( \alpha \)), and 13 (hypotenuse).

1. **Sine of \( \alpha \)**:
   \[
   \sin(\alpha) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{13}
   \]

2. **Cosine of \( \alpha \)**:
   \[
   \cos(\alpha) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{13}
   \]

3. **Tangent of \( \alpha \)**:
   \[
   \tan(\alpha) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{12}
   \]

### Triangle b:
- The triangle has sides 8 (opposite to angle \( \beta \)), 15 (adjacent to angle \( \beta \)), and 17 (hypotenuse).

1. **Sine of \( \beta \)**:
   \[
   \sin(\beta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{17}
   \]

2. **Cosine of \( \beta \)**:
   \[
   \cos(\beta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15}{17}
   \]

3. **Tangent of \( \beta \)**:
   \[
   \tan(\beta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{8}{15}
   \]

Let me know if you would like a more detailed explanation or have any questions. 

### Relative Questions:
1. How can trigonometric ratios help find unknown angles in a triangle?
2. What are the reciprocal trigonometric functions and how are they calculated?
3. How would the trigonometric ratios change if the sides of the triangles were scaled proportionally?
4. Can trigonometric functions be applied to non-right triangles? If so, how?
5. How can you determine the values of trigonometric functions without a calculator?

### Tip:
When dealing with right triangles, always remember that the hypotenuse is the longest side, opposite the right angle.

Temukan nilai-nilai perbandingan trigonometri dari segitiga-segitiga berikut.

Find the trigonometric ratios (sine, cosine, and tangent) of two given right triangles using the sides and the Pythagorean Theorem. This solution helps to calculate angles using trigonometry principles, suitable for students in Grades 9-11.

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