Use the formula A=12absinC 𝐴 = 1 2 𝑎 𝑏 sin ⁡ 𝐶 to find the area of △ABC △ 𝐴 𝐵 𝐶 to the nearest square yard if a=6 yards 𝑎 = 6 yards , b=12 yards 𝑏 = 12 yards , and ∠C=48 degrees ∠ 𝐶 = 48 degrees . (1 point) Responses 27 yards2 27 yards 2 27 yards squared 40 yards2 40 yards 2 40 yards squared 30 yards2 30 yards 2 30 yards squared 24 yards2

Question

GPT-4o mini · Answer

To find the area of 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 substituting the values into the formula:

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

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

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

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

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

Now multiply:

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

Rounding to the nearest square yard:

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

Therefore, the area of triangle ABC is:

27 yards².