Question

Area of Triangles Quick Check 5 of 55 of 5 Items Question Use the image to answer the 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 30 yards2 30 yards squared 27 yards2 27 yards squared 40 yards2 40 yards squared 24 yards2 24 yards squared Skip to navigation page 14 of 14

Answer 1

To find the area of triangle \( \triangle ABC \) using the formula \( A = \frac{1}{2}ab \sin C \), we can substitute the given values: \( a = 6 \) yards, \( b = 12 \) yards, and \( \angle C = 48^\circ \).

First, we calculate \( \sin 48^\circ \):

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

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

\[
\frac{1}{2} \times 6 \times 12 = \frac{72}{2} = 36
\]

Next, we need to multiply this by \( \sin 48^\circ \). Let's find the approximate value of \( \sin 48^\circ \):

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

Now, we can calculate the area:

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

Rounding to the nearest square yard gives us:

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

Thus, the area of triangle \( \triangle ABC \) is **27 yards²**.