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

30 yards2
30 yards squared

24 yards2
24 yards squared

40 yards2
40 yards squared

27 yards2

Answer 1

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

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

First, convert the angle \( C \) from degrees to radians if needed, but since we will use the sine function directly in degrees, that’s fine as well.

Now, substitute the values into the formula:

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

Calculating step-by-step:

1. Calculate \( \frac{1}{2} \times 6 \times 12 \):

\[
\frac{1}{2} \times 6 = 3
\]
\[
3 \times 12 = 36
\]

2. Now, calculate \( \sin(48^\circ) \). Using a calculator, we find:

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

3. Now, multiply:

\[
A \approx 36 \times 0.7431
\]
\[
A \approx 26.6756
\]

Rounding to the nearest square yard:

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

Thus, the area of triangle \( ABC \) to the nearest square yard is:

**27 yards²**

So the answer is:

**27 yards²**