A surveyor needs to measure the width of a building. He identifies two points [math]E[/math] and [math]F[/math] at ground level on opposite sides of the building. He then walks to a point a distance away from the building: point [math]G[/math]. He measures the distance from [math]E[/math] to [math]G[/math] as [math]284[/math] feet, the distance from [math]F[/math] to [math]G[/math] as [math]322[/math] feet, and the measure of [math]\angle G[/math] as [math]63^\circ[/math]. How wide is the building? Round your answer to the nearest foot, then determine whether it is reasonable given the context of the problem.

[list=1][br][*]Draw and label a sketch of the situation.[br][*]Find [math]EF[/math] using the Law of Cosines.[br][*]Determine if the answer is reasonable.[br][/list]