 # Solving a Triangle - SSA, SAS, SSS

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In this lesson, we will learn how to solve SSA, SAS and SSS triangles using the Law of Sines and Law of Cosines. Solving a triangle means to find all the unknown lengths and angles of the triangle.

How to solve SSA Triangles?
SSA (side-side-angle) means that we are given two sides and an angle that is not between the two sides.
1. Use the Law of Sines to calculate one of the other two angles. (Test for ambiguous case)
2. Find the third angle, since we know that angles in a triangle add up to 180°.
3. Use the Law of Sines again to find the unknown side.

How to solve SAS Triangles?
SAS (side-angle-side) means that we are given two sides and an angle that is between the two sides.
1. Use the Law of Cosines to calculate the unknown side.
2. Use the Law of Sines to find the unknown angle opposite the shorter side or use the Law of Cosines to find one of the unknown angles.
3. Find the third angle, since we know that angles in a triangle add up to 180°.

How to solve SSS Triangles?
SSS (side-side-side) means that we are given three sides.
1. Use the Law of Cosines to calculate one of the unknown angle.
2. Use the Law of Cosines again to find the other angle.
3. Find the third angle, since we know that angles in a triangle add up to 180°.

Solving a Triangle, SSA, Example 1
In this video, we find a missing side length using SSA and the law of sines.

Solving a Triangle, SSA, Ambiguous Case
Using the Law of Sines to solve SSA triangles. Single, double and no-solution cases.
Solving Triangles in SAS and SSS form

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