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The image shows two problems involving right triangles and trigonometric ratios.

### Problem 1: Example 2
Given the right triangle ABC with:
- Side \( a = 10 \)
- Side \( b = 12 \)
- Hypotenuse \( c = 16 \)

The trigonometric ratios for angle \( A \) are calculated as follows:

1. **Sine of \( A \)**: 
   \[
   \sin A = \frac{a}{c} = \frac{10}{16} = 0.625
   \]

2. **Cosine of \( A \)**: 
   \[
   \cos A = \frac{b}{c} = \frac{12}{16} = 0.75
   \]

3. **Tangent of \( A \)**: 
   \[
   \tan A = \frac{a}{b} = \frac{10}{12} \approx 0.8333
   \]

4. **Cotangent of \( A \)**: 
   \[
   \cot A = \frac{b}{a} = \frac{12}{10} = 1.2
   \]

5. **Secant of \( A \)**: 
   \[
   \sec A = \frac{c}{b} = \frac{16}{12} \approx 1.3333
   \]

6. **Cosecant of \( A \)**: 
   \[
   \csc A = \frac{c}{a} = \frac{16}{10} = 1.6
   \]

### Problem 2: Activity #1, Exercise 1.1
Given the right triangle ABC with:
- Side \( a = 35 \) cm
- Side \( b = 48 \) cm
- Hypotenuse \( c \) to be found.

Using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2} = \sqrt{35^2 + 48^2} = \sqrt{1225 + 2304} = \sqrt{3529}
\]

Calculating the value of \( c \):
\[
c \approx 59.4 \text{ cm}
\]

If you have any questions or need further explanation, let me know!

### Related Questions:
1. How do you find the trigonometric ratios of other angles in a right triangle?
2. How does the Pythagorean theorem help in solving right triangles?
3. What are the reciprocal trigonometric functions?
4. How do you calculate the angles if only side lengths are given?
5. What are the applications of trigonometric ratios in real-world problems?

### Tip:
Always double-check the hypotenuse value to ensure correct application of trigonometric ratios.

Given the right triangles, calculate the trigonometric ratios for the angles given the sides.

Learn how to calculate trigonometric ratios such as sine, cosine, tangent, and their reciprocals for right triangles. This problem involves using the Pythagorean theorem to determine missing sides and then applying trigonometric functions. Suitable for students in Grades 9-11.

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