Trigonometry

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Area, Navigation, Law of Cosines, Law of Sines, Bearings

TRIG-L97ED9

A farmer was preparing to fence in a plot of land. He placed a marker in the ground at $\text{point A}$ and then walked directly East for $\text{600 meters}$ where he placed a second marker at $\text{point B}$. The farmer then began to walk at a bearing of ${140}^{°}$ for another $\text{300 meters}$ where he placed a third marker, $\text{point C}$. The farmer next began to walk at a bearing of ${240}^{°}$ for an additional $\text{800 meters}$, where he placed his final marker, $\text{point D}$. The farmer then walked directly back to his original marker.

If the farmer were to enclose the property with a fence, with the four markers as the vertices, what is the area of the quadrilateral piece of land enclosed by the fence? (Round your answer to the nearest tenth $m^2$)

A

$170831.7\; { m }^{ 2 }$

B

$307122.20\; { m }^{ 2 }$

C

$236641.4\; { m }^{ 2 }$

D

$326513.9\; { m }^{ 2 }$