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To find the size of angle \( A \), we can use the **sine rule**, since we know two sides and the angle opposite one of them. The sine rule is given by:

\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]

Here:
- \( a = 9 \, \text{cm} \) (side opposite angle \( B = 38^\circ \)),
- \( b = 11 \, \text{cm} \),
- and we need to find angle \( A \).

We can first use the sine rule to find angle \( C \). The sine rule for angle \( C \) is:

\[
\frac{c}{\sin C} = \frac{a}{\sin B}
\]

\[
\frac{11}{\sin C} = \frac{9}{\sin 38^\circ}
\]

Let me calculate \( \sin C \) and then proceed to find angle \( A \).The measure of angle \( C \) is approximately \( 48.81^\circ \).

Now, to find angle \( A \), we can use the fact that the sum of angles in a triangle is always \( 180^\circ \). Thus:

\[
A = 180^\circ - B - C
\]

Let me calculate angle \( A \).The size of angle \( A \) is approximately \( 93.19^\circ \).

Would you like more details on the process or have any other questions? Here are some related questions to explore:

1. How can the sine rule be applied to other triangles?
2. What is the cosine rule, and when is it used?
3. How do you solve for angles in non-right triangles?
4. What are the different types of triangles, and how do they affect angle calculations?
5. How do angle properties in polygons differ from those in triangles?

**Tip:** Always remember that the angles of any triangle must sum to 180 degrees. This can help double-check your work!

Work out the size of angle A in the triangle where angle B = 38°, side AB = 11 cm, and side AC = 9 cm.

Learn how to calculate angle A in a triangle with sides of 11 cm and 9 cm and angle B = 38°. We apply the sine rule and use the angle sum theorem to find the unknown angle. This trigonometry problem is suitable for Grades 9-12 students.

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