Answer:
The area of the triangle is 231 cm² to the nearest square centimeter
Step-by-step explanation:
We can find the area of a triangle has the lengths of two sides and the measure of the included angle by using the trigonometry
A = [tex]\frac{1}{2}[/tex] × s1 × s2 × sinФ, where
- s1 and s2 are the two sides of the triangle
- Ф is the angle included between s1 and s2
In ΔABC
∵ AC = 24 cm
∴ s1 = 24
∵ BC = 30 cm
∴ s2 = 30
∵ m∠C = 40°
∴ Ф = 40°
→ By using the rule of the area above
∵ A = [tex]\frac{1}{2}[/tex] × 24 × 30 × sin(40°)
∴ A = 231.4035395 cm²
→ Round it to the nearest square centimeter
∴ A = 231 cm²
∴ The area of the triangle is 231 cm² to the nearest square centimeter
