Solving ASA Triangles
"ASA" means "Angle, Side, Angle"
This means we are given two angles and a side between the angles.
To solve an ASA Triangle
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 × sin76°)/sin70° = 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 × sin34°)/sin70° = 5.36 to 2 decimal places.
Now we have completely solved the triangle i.e. we have found all its angles and sides.
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
So y/sin(87°) = 18.9/sin(51°)
So y = (18.9 × sin(87°))/sin(51°) = 24.29 to 2 decimal places.
Similarly we can find z by using The Law of Sines:
z/sinZ = x/sin X
So z/sin(42°) = 18.9/sin(51°)
So a = (18.9 × sin(42°))/sin(51°) = 16.27 to 2 decimal places.