To find the area of triangle $PQR$, we can use the formula for the area of a triangle when two sides and the included angle are known:

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

Where:

• $a$ and $b$ are the lengths of two sides,
• $C$ is the included angle between them.

In this case:

• $a = 19 \, \text{cm}$ (side $PR$),
• $b = 17 \, \text{cm}$ (side $QR$),
• $C = 55^\circ$ (angle $\angle PQR$).

Now, I'll calculate the area using these values.The area of triangle $PQR$ is approximately $132.3 \, \text{cm}^2$.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you find the area of a triangle when only two sides and an angle are known?
2. How would the area change if angle $R$ were larger?
3. Can you find the perimeter of the triangle given the sides $PR$, $QR$, and $PQ$?
4. How can the Law of Sines be applied to this triangle?
5. What would happen if the angle were given in radians instead of degrees?

Tip: Always ensure your calculator is set to the correct mode (degrees or radians) when dealing with angles in trigonometry!