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

40 yards2
40 yards squared

24 yards2
24 yards squared

27 yards2
27 yards squared

30 yards2

Answer 1

To find the area of triangle \( \triangle ABC \) 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 substitute these values into the formula:

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

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

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

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

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

Now we can find the area \( A \):

\[
A \approx 36 \times 0.7431 \approx 26.69
\]

Rounding to the nearest square yard, we get:

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

Therefore, the area of triangle \( \triangle ABC \) is

**27 yards²** (or **27 yards squared**).