https://file.aiquickdraw.com/mathbot/file/17255481043998p4tndih.jpg

The image contains a problem related to a triangle LMN with the following given information:

- \( LM = 12.4 \, \text{mm} \)
- \( MN = 7.9 \, \text{mm} \)
- Angle \( \angle NLM = 28^\circ \)

The problem asks for the following:

**(a)** Given that angle \( MNL \) is acute, calculate the area of triangle LMN. Provide the answer to 3 significant figures.

### Solution:
We can use the formula for the area of a triangle when two sides and the included angle are known:

\[
\text{Area} = \frac{1}{2} \times LM \times MN \times \sin(\angle NLM)
\]

Now, let's calculate this step by step.

- \( LM = 12.4 \, \text{mm} \)
- \( MN = 7.9 \, \text{mm} \)
- \( \angle NLM = 28^\circ \)

I'll compute the area now.The area of triangle LMN is approximately \( 23.0 \, \text{mm}^2 \), rounded to 3 significant figures.

Would you like further details or have any questions?

Here are some related questions to explore:
1. How can you calculate the area of a triangle if you only know the base and height?
2. What is the sine rule and how is it used in triangles?
3. How does the cosine rule differ from the sine rule in solving triangles?
4. Can you calculate the perimeter of triangle LMN with the given information?
5. How would the area calculation change if \( \angle NLM \) were obtuse?

**Tip:** Always ensure that your calculator is in the correct mode (degrees or radians) when working with trigonometric functions!

In triangle LMN, LM = 12.4 mm, MN = 7.9 mm, and angle NLM = 28°. Given that angle MNL is acute, calculate the area of triangle LMN. Give your answer to 3 significant figures.

Learn how to calculate the area of triangle LMN with sides LM = 12.4 mm, MN = 7.9 mm, and an included angle of 28°. This problem demonstrates the application of the area formula for triangles using trigonometric functions. Ideal for students in Grades 9-11.

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