# 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 find the third angle using the three angles add to 180° then use The Law of Sines to find each of the other two sides.

### 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°':

So C = 180° − 76° − 34° = 70°

We can now find side a by using The Law of Sines:

a/sinA = c/sin C

a/sin76° = 9/sin70°

a = (9/sin70°) × sin76°
a = 9.29 to 2 decimal places

Similarly we can find side b by using The Law of Sines:

b/sinB = c/sin C

b/sin34° = 9/sin70°

b = (9/sin70°) × sin34°
b = 5.36 to 2 decimal places

Now we have completely solved the triangle i.e. we have found all its 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:

y/sinY = x/sin X

y/sin(87°) = 18.9/sin(51°)

y = (18.9/sin(51°)) × sin(87°)
y = 24.29 to 2 decimal places.

Similarly we can find z by using The Law of Sines:

z/sinZ = x/sin X

z/sin(42°) = 18.9/sin(51°)

z = (18.9/sin(51°)) × sin(42°)
z = 16.27 to 2 decimal places.