To calculate the area of the triangle in the image, we can use the formula for the area of a triangle given two sides and the included angle, which is:

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

Where:

• $a = 6 \, \text{m}$ (one side)
• $b = 7 \, \text{m}$ (the other side)
• $C = 55^\circ$ (the angle between these sides)

Now, I'll calculate the area using this formula.The area of the triangle is approximately 17.2 square meters, rounded to one decimal place.

Would you like further details or have any questions?

Here are some related questions to explore:

1. How do you calculate the area of a triangle if all three sides are given?
2. How can you find the third angle in a triangle when two angles are known?
3. What is the difference between using sine for angles in degrees versus radians?
4. How does the Law of Cosines relate to finding missing sides in triangles?
5. How can you calculate the height of a triangle if the area and base are known?

Tip: Always make sure to use radians when applying trigonometric functions in most calculators and programming languages.