Solving SSA Triangles
"SSA" means "Side, Side, Angle"
This means we are given two sides and an angle that is not the angle between the sides. 
To solve an SSA triangle

Example 1
In this triangle we know
 angle B = 31°
 b = 8
 and c = 13
In this case, we can use The Law of Sines first to find angle C:
sinC/c = sinB/b
sinC/13 = sin(31°)/8
So sinC = (13×sin(31°))/8
So C = sin^{1}(0.8369...)
Next, we can use 'angles of a triangle' to find angle A:
A = 180°  31°  56.818...°
Now we can use The Law of Sines again to find a:
a/sinA = b/sinB
So a/sin(92.181...°) = 8/sin(31°)
Did you notice that we didn't use A = 92.2°. That angle is rounded to 1 decimal place. It's much better to use the unrounded number 92.181...° which you should still have on your calculator screen from the last calculation.
So a = (sin(92.181...°) × 8)/sin(31°)
So, we have completely solved the triangle ...
... or have we?
Back when we calculated:
So C = sin^{1}(0.8369...)
We didn't think that sin^{1}(0.8369...) might have two answers (see Law of Sines)
The other answer for C is 180°  56.818...°
So let's go back and continue our example:
The other possible angle is:
C = 180°  56.818...°
With a new value for C we should also recalculate angle A and side a
Use 'angles of a triangle add to 180°' to find angle A:
A = 180°  31°  123.181...°
Now we can use The Law of Sines again to find a:
a/sinA = b/sinB
So a/sin25.818...° = 8/sin31°
So a = (sin25.818...°×8)/sin31°
Here you can see why we have two possible answers:
By swinging side "8" left and right we can
join up
with side "a" in two possible locations.
Example 2
This is also an SSA triangle.
In this triangle we know angle angle M = 125°, m = 12.4 and l = 7.6
We will use The Law of Sines to find angle L first:
sinL/l = sinM/m
sinL/7.6 = sin125°/12.4
So sinL = (7.6×sin125°)/12.4
So L = 30.136...°
Next, we will use 'angles of a triangle' to find angle N:
N = 180°  125°  30.136...°
Now we will use The Law of Sines again to find n:
n/sinN = m/sinM
So n/sin24.863...° = 12.4/sin125°
So n = (sin24.863...°×12.4)/sin125°
Note there is only one answer in this case. The "12.4" line only joins up one place. The other "possible" answer for L would be 149.9° which is impossible. We already have M = 125° and we can't have two obtuse angles in a triangle (they would add to more than 180°) 
Conclusion:
When solving a "Side, Side, Angle" triangle you need to
check if there might be another possible answer!