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)Responses24 yards224 yards squared30 yards230 yards squared27 yards227 yards squared40 yards2
Answers
GPT-4o mini
To find the area of triangle \( ABC \) using the formula \( A = \frac{1}{2}ab \sin C \), where \( a = 6 \) yards, \( b = 12 \) yards, and \( \angle C = 48^\circ \):
1. Plug in the values into the formula:
\[
A = \frac{1}{2} \times 6 \times 12 \times \sin(48^\circ)
\]
2. Calculate \( \frac{1}{2} \times 6 \times 12 \):
\[
\frac{1}{2} \times 6 = 3
\]
\[
3 \times 12 = 36
\]
So, \( A = 36 \times \sin(48^\circ) \).
3. Now, calculate \( \sin(48^\circ) \). (For this, you can use a calculator.)
\[
\sin(48^\circ) \approx 0.7431
\]
4. Substitute this value back into the area formula:
\[
A \approx 36 \times 0.7431 \approx 26.6776
\]
5. Round the area to the nearest square yard:
\[
A \approx 27 \text{ square yards}
\]
Thus, the area of triangle \( ABC \) to the nearest square yard is \( \boxed{27} \) square yards.
1. Plug in the values into the formula:
\[
A = \frac{1}{2} \times 6 \times 12 \times \sin(48^\circ)
\]
2. Calculate \( \frac{1}{2} \times 6 \times 12 \):
\[
\frac{1}{2} \times 6 = 3
\]
\[
3 \times 12 = 36
\]
So, \( A = 36 \times \sin(48^\circ) \).
3. Now, calculate \( \sin(48^\circ) \). (For this, you can use a calculator.)
\[
\sin(48^\circ) \approx 0.7431
\]
4. Substitute this value back into the area formula:
\[
A \approx 36 \times 0.7431 \approx 26.6776
\]
5. Round the area to the nearest square yard:
\[
A \approx 27 \text{ square yards}
\]
Thus, the area of triangle \( ABC \) to the nearest square yard is \( \boxed{27} \) square yards.