in triangle xyz angle y = 77 line segment xy = 10 and xz =11 what is the measure of angle z
+130518 x 11 z
10
y
77
We have a SSA situation, here........z could have two possible values
First, let's use the Law of Sines to find one value for z
sin y / xz = sinz / xy
sin (77) / 11 = sin z / 10
10*sin (77) / 11 = sin z use the sin inverse to find z
sin-1 [ 10*sin(77) / 11 ] = z = about 62.35°
The other possible value for z = [180 - 62.35]° = 117.65°
However, when this is added to the known angle of 77°, we have a triangle whose interior angles would sum to more than 180°.......so 62.35° is the only possibility for z
