Question

Use the formula A=12absinC 𝐴 = 1 2 𝑎 𝑏 sin ⁡ 𝐶 to determine the area of △ABC △ 𝐴 𝐵 𝐶 . What is the area to the nearest square inch if a=16 inches 𝑎 = 16 inches , b=18 inches 𝑏 = 18 inches , and ∠C=43 degrees ∠ 𝐶 = 43 degrees ? (1 point) Responses 98 inches2 98 inches 2 98 inches squared 196 inches2 196 inches 2 196 inches squared 105 inches2 105 inches 2 105 inches squared 134 inches2

Answer 1

To find the area \( A \) of triangle \( ABC \) using the formula:

\[ A = \frac{1}{2} a b \sin C \]

we will plug in the values:

• \( a = 16 \) inches
• \( b = 18 \) inches
• \( C = 43^\circ \)

First, we calculate \( \sin(43^\circ) \). Using a calculator, we find:

\[ \sin(43^\circ) \approx 0.6820 \]

Now we can substitute these values into the area formula:

\[ A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ) \]

Calculating it step by step:

1. Calculate \( \frac{1}{2} \times 16 \times 18 \):

\[ \frac{1}{2} \times 16 = 8 \]

\[ 8 \times 18 = 144 \]

2. Now, multiply by \( \sin(43^\circ) \):

\[ A = 144 \times 0.6820 \approx 98.208 \]

Therefore, the area \( A \) to the nearest square inch is:

\[ \boxed{98} \text{ inches}^2 \]

So the correct response is 98 inches².