Answer
$732$ ft$^{2}$
Work Step by Step
The area of the triangle is half the product of the length of two sides and the sine of the angle included between them:
$Area=\frac{1}{2}ab \sin C$
We substitute the values of $A,b$ and $c$ in this formula and solve:
$Area=\frac{1}{2}ab \sin C$
$Area=\frac{1}{2}(35.1)(43.8) \sin 72.2^{\circ}$
$Area=\frac{1}{2}(1537.38) \sin 72.2^{\circ}$
$Area=768.69 \sin 72.2^{\circ}$
Using a calculator, $\sin 72.2^{\circ}=0.9521$. Therefore,
$Area=768.69 \sin 72.2^{\circ}$
$Area=768.69(0.9521)$
$Area=731.89\approx732$
Therefore, the area of the triangle is $732$ ft$^{2}$.
