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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

30 yards2
30 yards squared

40 yards2
40 yards squared

Answer 1

To find the area of triangle \( ABC \) using the formula

\[ A = \frac{1}{2}ab \sin C, \]

we need to plug in the values for \( a \), \( b \), and \( \angle C \).

Given:

• \( a = 6 \) yards
• \( b = 12 \) yards
• \( \angle C = 48^\circ \)

Now, we calculate \( \sin C \):

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

Now we can plug in the values into the area formula:

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

Calculating it step by step:

1. Calculate \( \frac{1}{2} \times 6 \times 12 \): \[ \frac{1}{2} \times 6 \times 12 = \frac{72}{2} = 36 \]

2. Now multiply by \( \sin(48^\circ) \): \[ A = 36 \times 0.7431 \approx 26.70 \]

Rounding to the nearest square yard, the area \( A \) is approximately \( 27 \) square yards.

Thus, the answer is:

27 yards² (or 27 yards squared).