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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!

Find the area of the triangle PQR, where PR = 19 cm, QR = 17 cm, and angle R = 55°.

This page explains how to calculate the area of triangle PQR using trigonometric principles, where PR = 19 cm, QR = 17 cm, and the angle between them (angle R) is 55°. Step-by-step guidance for students in Grades 9-11, involving sine functions.

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