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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 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
196 inches squared

Answer 1

To calculate the area of triangle \( \triangle ABC \) using the formula \( A = \frac{1}{2} a b \sin C \), we need to plug in the values given:

• \( a = 16 \) inches
• \( b = 18 \) inches
• \( C = 43^\circ \)

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

\[ \sin(43^\circ) \approx 0.681998 \]

Now, we can substitute the values into the area formula:

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

Calculating inside the formula:

\[ A = \frac{1}{2} \times 16 \times 18 \times 0.681998 \]

Calculating \( 16 \times 18 = 288 \):

\[ A = \frac{1}{2} \times 288 \times 0.681998 \] \[ A = 144 \times 0.681998 \approx 98.018 \]

Rounding to the nearest square inch:

\[ A \approx 98 \text{ inches}^2 \]

Thus, the area of triangle \( \triangle ABC \) to the nearest square inch is \( 98 \) inches².

The correct response is:

98 inches²