Use the formula A=12absinC to determine the area of △ABC. What is the area to the nearest square inch if a=16 inches, b=18 inches, and ∠C=43 degrees?

(1 point)
Responses

98 inches2
98 inches squared

134 inches2
134 inches squared

105 inches2
105 inches squared

196 inches2

1 answer

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

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

we will substitute \( a = 16 \) inches, \( b = 18 \) inches, and \( \angle C = 43^\circ \).

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

\[ \sin 43^\circ \approx 0.681998. \]

Now, substitute the values into the area formula:

\[ A = \frac{1}{2} \times 16 \times 18 \times \sin(43^\circ). \]

Calculating this step-by-step:

  1. Calculate \( \frac{1}{2} \times 16 \):

\[ \frac{1}{2} \times 16 = 8. \]

  1. Calculate \( 8 \times 18 \):

\[ 8 \times 18 = 144. \]

  1. Now multiply by \( \sin(43^\circ) \):

\[ A = 144 \times 0.681998 \approx 98.081. \]

To the nearest square inch, the area \( A \) is approximately \( 98 \) square inches.

The correct response is:

98 inches²