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What is the area of the triangle below to 3 significant figures? m³ to 3 s.f.

To find the area of the triangle shown in the image, we can use the formula for the area of a triangle given two sides and the included angle between them:

\[
\text{Area} = \frac{1}{2}ab\sin(C)
\]

Where:
- \(a\) and \(b\) are the lengths of two sides.
- \(C\) is the included angle between these sides.

From the diagram:
- \(a = 2.3 \, \text{m}\)
- \(b = 0.45 \, \text{m}\)
- \(C = 27^\circ\)

Now, let's compute the area.The area of the triangle is approximately \(0.235 \, \text{m}^2\) to three significant figures.

Would you like any further details or clarifications?

Here are 5 related questions:
1. How would the area change if the angle increased to \(45^\circ\)?
2. What would happen to the area if the second side increased to \(0.6 \, \text{m}\)?
3. Can you use other trigonometric rules to find the area in a different way?
4. How can you find the height of the triangle from the base using trigonometry?
5. What is the relationship between the area and the sine of the included angle?

**Tip**: When solving for areas in triangles, always ensure you use angles in the correct units (degrees or radians) depending on your calculator's settings.

What is the area of the triangle below to 3 significant figures? m³ to 3 s.f.

Find the area of a triangle with sides 2.3 m and 0.45 m and an included angle of 27 degrees using trigonometry. Step-by-step solution including the formula 1/2 * a * b * sin(C), suitable for students in Grades 9-12.

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