Question

A triangle upper A upper B upper C. The edge upper A upper B is labeled c. The edge upper A upper C is labeled b. The edge upper B upper C is labeled a.
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

27 yards2
27 yards squared

40 yards2
40 yards squared

30 yards2

Answer 1

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

- \( a = 6 \, \text{yards} \)
- \( b = 12 \, \text{yards} \)
- \( \angle C = 48^\circ \)

Now we can plug these values into the formula:

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

Calculating the sine of \( 48^\circ \):

\[
\sin(48^\circ) \approx 0.7431 \quad \text{(using a calculator)}
\]

Now substituting this value into the area formula:

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

Calculating the product:

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

Now multiplying by \( \sin(48^\circ) \):

\[
A \approx 36 \times 0.7431 \approx 26.68
\]

Rounding to the nearest square yard gives:

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

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

**27 yards²**