Answer
$722.9$ in$^{2}$
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:
$Area=\frac{1}{2}bc \sin A$
We substitute the values of $A,b$ and $c$ in this formula and solve:
$Area=\frac{1}{2}bc \sin A$
$Area=\frac{1}{2}(32.67)(52.89) \sin 56.80^{\circ}$
$Area=\frac{1}{2}(1727.92) \sin 56.80^{\circ}$
$Area=863.96\sin 56.80^{\circ}$
Using a calculator, $\sin 56.80^{\circ}=0.83676$. Therefore,
$Area=863.96\sin 56.80^{\circ}$
$Area=863.96(0.83676)$
$Area=722.93\approx722.9$
Therefore, the area of the triangle is $722.9$ in$^{2}$.
