Question

Use the formula A=12absinC 𝐴 = 1 2 𝑎 𝑏 sin ⁡ 𝐶 to find the area of △ABC △ 𝐴 𝐵 𝐶 to the nearest square yard if a=6 yards 𝑎 = 6 yards , b=12 yards 𝑏 = 12 yards , and ∠C=48 degrees ∠ 𝐶 = 48 degrees . (1 point) Responses 27 yards2 27 yards 2 27 yards squared 40 yards2 40 yards 2 40 yards squared 30 yards2 30 yards 2 30 yards squared 24 yards2

Answer 1

To find the area of triangle ABC using the formula \( A = \frac{1}{2}ab \sin C \), we can substitute the values given:

- \( a = 6 \) yards
- \( b = 12 \) yards
- \( C = 48^\circ \)

Now substituting the values into the formula:

\[
A = \frac{1}{2} \times 6 \times 12 \times \sin(48^\circ)
\]

First, calculate \( \frac{1}{2} \times 6 \times 12 \):

\[
\frac{1}{2} \times 6 \times 12 = 36
\]

Next, calculate \( \sin(48^\circ) \). Using a calculator:

\[
\sin(48^\circ) \approx 0.7431
\]

Now multiply:

\[
A = 36 \times 0.7431 \approx 26.6696
\]

Rounding to the nearest square yard:

\[
A \approx 27 \text{ yards}^2
\]

Therefore, the area of triangle ABC is:

**27 yards².**