Questions: Unit Exam - Area Find the area of this triangle. Round to the nearest tenth. Submit

Solution Steps

The problem provides the lengths of two sides of the triangle and the included angle:

• Side \( a = 9 \) ft
• Side \( b = 20 \) ft
• Included angle \( C = 110^\circ \)

The formula to find the area \( A \) of a triangle when two sides and the included angle are known is: \[ A = \frac{1}{2}ab \sin(C) \]

Substitute \( a = 9 \) ft, \( b = 20 \) ft, and \( C = 110^\circ \) into the formula: \[ A = \frac{1}{2} \times 9 \times 20 \times \sin(110^\circ) \]

Using a calculator, find \( \sin(110^\circ) \): \[ \sin(110^\circ) \approx 0.9397 \]

Calculate the area: \[ A = \frac{1}{2} \times 9 \times 20 \times 0.9397 \] \[ A = \frac{1}{2} \times 180 \times 0.9397 \] \[ A = 90 \times 0.9397 \] \[ A \approx 84.573 \]

Round the result to the nearest tenth: \[ A \approx 84.6 \]

Final Answer