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To find the length of \( AB \) in the diagram, we can use trigonometric relationships. The triangle \( \triangle ABC \) is a right triangle with the following information provided:

- \( \angle A = 70^\circ \)
- \( \angle B = 30^\circ \)
- Side \( AC = 10.6 \) m (opposite to \( \angle B \))
- Side \( BC = 20 \) m (hypotenuse)

We can use the sine rule or cosine rule to find the length of side \( AB \). But since we have a right triangle, we can directly use trigonometric ratios.

### Using the sine rule:
\[
\frac{AB}{\sin(70^\circ)} = \frac{20 \text{ m}}{\sin(90^\circ)} = \frac{AB}{\sin(70^\circ)} = \frac{20 \text{ m}}{1}
\]
Thus,
\[
AB = 20 \times \sin(70^\circ)
\]

### Calculating the length:
\[
AB = 20 \times \sin(70^\circ) \approx 20 \times 0.9397 \approx 18.79 \text{ m}
\]

So, the length of \( AB \) is approximately **18.79 meters**.

Would you like more details, or do you have any questions?

### Related Questions:
1. What are the other trigonometric ratios for \( \angle A = 70^\circ \) in this triangle?
2. How can we verify the length of \( AB \) using the Pythagorean theorem?
3. What is the area of the triangle \( \triangle ABC \)?
4. How would the length \( AB \) change if \( \angle A \) was increased to \( 80^\circ \)?
5. How can we find the length of the altitude from \( C \) to \( AB \)?

### Tip:
Always ensure the angles in any triangle add up to \( 180^\circ \) when solving for unknowns, especially in right triangles.

Learn how to find the length of side AB in a right triangle with angles 70 degrees and 30 degrees using trigonometric ratios. The solution involves applying the sine rule and understanding basic trigonometric relationships. Suitable for high school students studying trigonometry.

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