To find the area of this triangle, we can use the SAS (Side-Angle-Side) formula for area:

$\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)$

where:

• $a = 4.7$
• $b = 2.8$
• $C = 22^\circ$

Let's substitute these values and calculate:

$\text{Area} = \frac{1}{2} \times 4.7 \times 2.8 \times \sin(22^\circ)$

1. First, calculate $\sin(22^\circ)$.
2. Multiply $4.7 \times 2.8$.
3. Multiply that result by $\sin(22^\circ)$.
4. Finally, multiply by $\frac{1}{2}$ to get the area.

Let me solve this for you.The area of the triangle is approximately $2.46 \, \text{units}^2$.

Would you like further details on this calculation, or have any questions?

Here are some related questions for further exploration:

1. How would the area change if the angle increased?
2. What other methods can be used to find the area if all angles and sides are known?
3. How can trigonometric identities simplify area calculations for triangles?
4. How would this formula apply to obtuse triangles?
5. Can the SAS formula be used for non-triangular shapes?

Tip: When using trigonometric functions, ensure your calculator is set to the correct mode (degrees or radians) based on the angle's units.