Question

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

Answer 1

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

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

Now, let’s calculate the area:

1. First, calculate \( \sin C \):
\[
\sin 48^\circ \approx 0.7431 \quad \text{(using a calculator)}
\]

2. Substitute the values into the area formula:
\[
A = \frac{1}{2} \times 6 \times 12 \times \sin(48^\circ)
\]
\[
A = \frac{1}{2} \times 6 \times 12 \times 0.7431
\]
\[
A = 36 \times 0.7431
\]
\[
A \approx 26.6716
\]

3. Rounding to the nearest square yard:
\[
A \approx 27 \text{ yards squared}
\]

Thus, the area of triangle \( \triangle ABC \) is approximately **27 yards squared**.