Solving AAS Triangles
"AAS" means "Angle, Angle, Side"
This means we are given two angles and one side (which is not between the angles). 
To solve an AAS triangle

Example 1
In this triangle we know:
 angle A = 35°
 angle C = 62°
 and side c = 7
It's easy to find angle B by using 'angles of a triangle add to 180°':
B = 180°  35°  62° = 83°
We can also find side a by using The Law of Sines:
a/sin A = c/sin C
a/sin(35°) = 7/sin(62°)
a = (7 × sin(35°))/sin(62°) = 4.55 (to 2 decimal places).
Also we can find b by using The Law of Sines:
b/sin B = c/sin C
b/sin(83°) = 7/sin(62°)
b = (7 × sin(83°))/sin(62°) = 7.87 to 2 decimal places.
Now we have completely solved the triangle!
Did you notice that we used b/sin B = c/sin C rather than b/sin B = a/sin A for the last calculation?
There's a good reason for that. What if we had made a mistake in finding a? Then our answer for b would also be wrong!
As a rule, it is always better to use the sides and angles that are given rather than ones we've just worked out.
Example 2
This is also an AAS triangle.
First find angle A by using 'angles of a triangle add to 180°':
Now find side c by using The Law of Sines:
Similarly we can find side a by using The Law of Sines and using the given side b = 12.6 rather than c that we just worked out:
Done!