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The image you provided shows a triangle with sides \( AB = 15 \) cm, \( AC = 10 \) cm, and an angle \( \angle CAB = 30^\circ \). The problem asks to find the area of the triangle \( \triangle ABC \).

### Solution:

To find the area of \( \triangle ABC \), we can use the **formula for the area of a triangle when two sides and the included angle are known**:

\[
\text{Area} = \frac{1}{2} \times AB \times AC \times \sin(\angle CAB)
\]

### Given:
- \( AB = 15 \) cm
- \( AC = 10 \) cm
- \( \angle CAB = 30^\circ \)

### Step 1: Calculate the sine of \( 30^\circ \).

\[
\sin(30^\circ) = \frac{1}{2}
\]

### Step 2: Plug in the values into the area formula.

\[
\text{Area} = \frac{1}{2} \times 15 \times 10 \times \frac{1}{2}
\]

\[
\text{Area} = \frac{1}{2} \times 150 \times \frac{1}{2} = \frac{150}{4} = 37.5 \text{ cm}^2
\]

### Final Answer:
The area of the triangle \( \triangle ABC \) is \( 37.5 \) square centimeters.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How would you find the area of a triangle if all three sides are known?
2. What is the significance of the sine function in calculating the area of a triangle?
3. How would the area change if \( \angle CAB \) was \( 60^\circ \) instead of \( 30^\circ \)?
4. Can the area formula using sine be applied to non-right triangles? Why?
5. How would you calculate the area if only the three angles and one side are known?

**Tip:** Remember, the sine function for angles greater than \( 90^\circ \) can be negative, which will affect the calculated area if not handled correctly. Always ensure the angle is within the appropriate range when applying this formula.

Find the area of triangle ABC given AB = 15 cm, AC = 10 cm, and ∠CAB = 30°.

Learn how to find the area of triangle ABC using the given sides AB = 15 cm, AC = 10 cm, and angle CAB = 30°. This problem covers key concepts in geometry and trigonometry, including the sine rule. Suitable for students in Grades 8-10.

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