For the third angle, we could just subtract angle A and Angle B from 180°, but let's use the Law of Sines again.

(sine (A) / side a) = (sine (C) / side c)

(sine (21.787) / 15) = (sine (C) / 25)

sine (C) = (0.37116 * 25) / 15

sine (C) = 0.6186

Angle C = 38.214°
Just to make sure that everything was calculated correctly, we should add up angles A, B and C and they should total 180°.
However, 21.787 plus 60.00 plus 38.214 sums to 120° so something has gone awry.

When we take the arc sine of a number, we actually get *two* angles that are between zero and 180°.
(For example, the arc sine of .5 equals 30° and 150°).

That means angle B *could* be (180 -60) or 120° *and* angle C *could* be (180 -38.214) or 141.786°.

It can be seen that it is angle B that is actually 120° because that makes all 3 angles sum to 180°.

*So, is there any way that we can avoid the ambiguous case?*

Actually there are several.

1) When you calculate the first angle using the Law of Cosines, *always* calculate the largest angle. (The largest angle will be the angle opposite the largest side.)

2) When using the Law of Sines, *never* use it to calculate the largest angle.

3) *Always* use the Law of Cosines for the calculations. Granted it's a little more difficult but you can be sure of the results.