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To calculate the area of triangle \( ABC \), we can use the formula:

\[
\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)
\]

where:
- \( a = 6 \, \text{cm} \) (side \( AB \)),
- \( b = 5 \, \text{cm} \) (side \( BC \)),
- \( C = 40^\circ \) (angle \( \angle ACB \)).

Now, let's compute the area:

\[
\text{Area} = \frac{1}{2} \times 6 \times 5 \times \sin(40^\circ)
\]

I'll calculate this for you.The area of triangle \( ABC \) is approximately \( 9.64 \, \text{cm}^2 \) when rounded to three significant figures.

Would you like more details or have any questions?

Here are some related questions:

1. How would the area change if angle \( \angle ACB \) were increased to \( 50^\circ \)?
2. Can you calculate the area if you were given the length of \( AC \) instead of \( BC \)?
3. How can you use the Law of Sines to find the remaining angles in triangle \( ABC \)?
4. What is the perimeter of triangle \( ABC \)?
5. How would you calculate the area if \( \angle BAC \) were given instead of \( \angle ACB \)?

**Tip:** Remember that the sine function reaches its maximum value at \( 90^\circ \). This implies that for a fixed base and height, the area of a triangle is maximized when the angle between them is \( 90^\circ \).

Calculate the area of triangle ABC, where AB = 6 cm, BC = 5 cm, and angle ACB = 40°. Give your answer correct to 3 significant figures.

Learn how to calculate the area of triangle ABC with sides AB = 6 cm, BC = 5 cm, and angle ACB = 40° using the formula Area = 1/2 * a * b * sin(C). This solution includes step-by-step trigonometric calculations, suitable for students in Grades 9-11.

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