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To calculate the area of the triangle, we can use the formula for the area of a triangle when two sides and the included angle are given:

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

Where:
- \( a = 16 \, \text{mm} \) (one side)
- \( b = 11 \, \text{mm} \) (another side)
- \( \theta = 14.4^\circ \) (the included angle)

Now, let's calculate the area:

\[
\text{Area} = \frac{1}{2} \times 16 \times 11 \times \sin(14.4^\circ)
\]

First, we need to calculate \( \sin(14.4^\circ) \). Using a calculator:

\[
\sin(14.4^\circ) \approx 0.2487
\]

Now substitute this value into the formula:

\[
\text{Area} = \frac{1}{2} \times 16 \times 11 \times 0.2487
\]

\[
\text{Area} \approx 21.85 \, \text{mm}^2
\]

Therefore, the area of the triangle is approximately **21.85 mm²** to two decimal places.

Would you like more details on any step, or do you have any questions? Here are some related questions to explore:

1. How is the sine of an angle calculated in trigonometry?
2. What other methods can be used to find the area of a triangle?
3. How can we find the area of a triangle if all three sides are known?
4. Why does the formula use the sine of the angle?
5. How do trigonometric identities help in solving geometry problems?

**Tip:** Always ensure your calculator is in degree mode when calculating trigonometric functions for angles measured in degrees!

Given that θ = 14.4°, calculate the area of the triangle below. Give your answer to 2 d.p.

Find the area of a triangle with sides 16 mm and 11 mm, and an included angle of 14.4°. This problem uses trigonometric formulas to calculate the area of a non-right triangle, suitable for students in Grades 9-11.

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