To find the area of the given triangle, we will use the formula for the area of a triangle with two sides and the included angle:

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

Where:

• $a = 15 \, \text{m}$ (one side)
• $b = 22 \, \text{m}$ (another side)
• $C = 115^\circ$ (the included angle)

Step 1: Plug in the values

$\text{Area} = \frac{1}{2} \cdot 15 \cdot 22 \cdot \sin(115^\circ)$

Step 2: Calculate $\sin(115^\circ)$

Using a calculator or trigonometric tables: $\sin(115^\circ) \approx 0.9063$

Step 3: Compute the area

$\text{Area} = \frac{1}{2} \cdot 15 \cdot 22 \cdot 0.9063$

$\text{Area} = 7.5 \cdot 22 \cdot 0.9063$

$\text{Area} \approx 149.54 \, \text{m}^2$

Step 4: Round to the nearest tenth

$\text{Area} \approx 149.5 \, \text{m}^2$

Final Answer:

The area of the triangle is 149.5 m².

Would you like a step-by-step explanation of how to use a calculator for this?
Here are 5 related questions for practice:

1. How do you find the area of a triangle when all sides are known?
2. What is the formula for $\sin(x)$ in terms of a unit circle?
3. How would the area change if the angle $C$ were $90^\circ$?
4. Can you compute the area using Heron's formula instead?
5. Why is $\sin(115^\circ)$ positive?

Tip: Remember to always double-check your calculator settings to ensure it is in degree mode when working with angles like $115^\circ$.