use the formula A=1/2absinC to determine the area of triangle ABC. what is the area to the nearest square inch if a = 16 inches, b= 18 inches, and angle C = 43 degrees?

1 answer

To find the area of triangle ABC using the formula \( A = \frac{1}{2}ab \sin C \), we can plug in the values for \( a \), \( b \), and \( C \).

Given:

  • \( a = 16 \) inches
  • \( b = 18 \) inches
  • \( C = 43^\circ \)
  1. First, calculate \( \sin C \): \[ \sin(43^\circ) \approx 0.681998 \]

  2. Now plug the values into the formula: \[ A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ) \] \[ A = \frac{1}{2} \times 16 \times 18 \times 0.681998 \]

  3. Calculate \( \frac{1}{2} \times 16 \times 18 \): \[ \frac{1}{2} \times 16 = 8 \] \[ 8 \times 18 = 144 \]

  4. Now multiply this by \( \sin(43^\circ) \): \[ A = 144 \times 0.681998 \approx 98.152 \]

  5. Finally, round the area to the nearest square inch: \[ A \approx 98 \text{ square inches} \]

Thus, the area of triangle ABC is approximately \( \boxed{98} \) square inches.