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

27 yards2
27 yards squared

24 yards2
24 yards squared

30 yards2
30 yards squared

40 yards2

Answer 1

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

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

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

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

Now, substitute the values into the area formula:

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

\[
A = \frac{1}{2} \times 6 \times 12 \times 0.7431
\]

Calculating the product:

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

Rounding to the nearest square yard:

\[
A \approx 27 \text{ square yards}
\]

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

The correct response is:

**27 yards²**