For [math]\triangle ABC[/math], find the measure of angle [math]C[/math] if [math]m\angle A = 34^\circ[/math], [math]c = 9[/math] meters, and [math]a = 7[/math] meters.

[list=1][br][*]Substitute the known values into the Law of Sines.[br][*]Determine which two fractions are necessary for solving the equation and then solve.[br][*]Use your calculator to find [math]m\angle C[/math].[br][*]Determine whether the ambiguous case is possible to determine if there is a second valid answer.[br][*]Determine the second valid measure of angle [math]C[/math].[br][/list]