Solving ASA Triangles
"ASA" means "Angle, Side, Angle"
"ASA" is when we know two angles and a side between the angles. 
To solve an ASA Triangle

Example 1
In this triangle we know:
 angle A = 76°
 angle B = 34°
 and c = 9
It's easy to find angle C by using 'angles of a triangle add to 180°':
C = 180° − 76° − 34° = 70°
We can now find side a by using the Law of Sines:
\frac{a}{sin(A)} = \frac{c}{sin(C)}
\frac{a}{sin(76°)} = \frac{9}{sin(70°)}
a = sin(76°) × \frac{9}{sin(70°)}
a = 9.29 to 2 decimal places
Similarly we can find side b by using the Law of Sines:
\frac{b}{sin(B)} = \frac{c}{sin(C)}
\frac{b}{sin(34°)} = \frac{9}{sin(70°)}
b = sin(34°) × \frac{9}{sin(70°)}
b = 5.36 to 2 decimal places
Now we have completely solved the triangle: we have found all angles and sides.
Example 2
This is also an ASA triangle.
First find angle X by using 'angles of a triangle add to 180°':
X = 180° − 87° − 42° = 51°
Now find side y by using the Law of Sines:
\frac{y}{sin(Y)} = \frac{x}{sin(X)}
\frac{y}{sin(87°)} = \frac{18.9}{sin(51°)}
y = sin(87°) × \frac{18.9}{sin(51°)}
y = 24.29 to 2 decimal places.
Similarly we can find z by using the Law of Sines:
\frac{z}{sin(Z)} = \frac{x}{sin(X)}
\frac{z}{sin(42°)} = \frac{18.9}{sin(51°)}
z = sin(42°) × \frac{18.9}{sin(51°)}
z = 16.27 to 2 decimal places.
All done!