Answer
$289.9$ m$^{2}$
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:
$Area=\frac{1}{2}bc \sin A$
$Area=\frac{1}{2}(35.29)(28.67) \sin 34.97^{\circ}$
$Area=\frac{1}{2}(1011.76) \sin 34.97^{\circ}$
$Area=505.88\sin 34.97^{\circ}$
Using a calculator, $\sin 34.97^{\circ}=0.57315$. Therefore,
$Area=505.88\sin 34.97^{\circ}$
$Area=505.88(0.57315)$
$Area=289.94\approx289.9$
Therefore, the area of the triangle is $289.9$ m$^{2}$.
