Question

use the formula ( a = \frac{1}{2}absin c ) to determine the area of ( \triangle abc ). what is the area to the nearest square inch if ( a = 16 ) inches, ( b = 18 ) inches, and ( angle c = 43 ) degrees?
(1 point)
( \bigcirc ) 98 inches²
( \bigcirc ) 158 inches²
( \bigcirc ) 110 inches²
( \bigcirc ) 100 inches²

Explanation:

Step1: Identify given values

We know \( a = 16 \) inches, \( b = 18 \) inches, and \( \angle C=43^\circ \). The formula for the area \( A \) of a triangle is \( A=\frac{1}{2}ab\sin C \).

Step2: Substitute values into formula

Substitute \( a = 16 \), \( b = 18 \), and \( \sin(43^\circ) \) into the formula:
\( A=\frac{1}{2}\times16\times18\times\sin(43^\circ) \)

Step3: Calculate step by step

First, calculate \( \frac{1}{2}\times16\times18 \):
\( \frac{1}{2}\times16\times18 = 8\times18=144 \)

Then, find \( \sin(43^\circ) \approx 0.6820 \)

Now, multiply \( 144 \) by \( 0.6820 \):
\( 144\times0.6820 = 98.208 \approx 98 \) (rounded to the nearest whole number)

Answer:

98 inches²