To solve for the area of triangle RPQ, we will use the formula for the area of a triangle when two sides and the included angle are known:
[tex]\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \][/tex]
where:
- [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of two sides of the triangle
- [tex]\( C \)[/tex] is the included angle between those sides
Given in the problem:
- RP = 8.7 cm
- PQ = 5.2 cm
- Angle PRQ = 32°
We'll follow these steps:
1. Convert the angle from degrees to radians:
[tex]\[
\text{Angle PRQ in radians} = \frac{32 \times \pi}{180}
\][/tex]
This gives an angle of approximately 0.5585053606381855 radians.
2. Calculate the area using the given formula:
[tex]\[
\text{Area} = \frac{1}{2} \times 8.7 \times 5.2 \times \sin(0.5585053606381855)
\][/tex]
This results in an area of approximately 11.986773756955094 square centimeters.
3. Round the area to 3 significant figures:
[tex]\[
\text{Rounded Area} = 11.987
\][/tex]
Therefore, the area of triangle RPQ, correct to 3 significant figures, is 11.987 square centimeters.
