Solving Triangles
What does "Solving a Triangle" mean? To solve a triangle means to find all unknown sides and angles when given enough information (at least 3 pieces, including at least one side).
Key Tools for Solving Triangles
1. The Law of Sines
Used when you know: AAS, ASA, or SSA (two angles and a side, or two sides and an angle opposite one of them).
$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$
Where $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively.
2. The Law of Cosines
Used when you know: SAS or SSS (two sides and the included angle, or all three sides).
$$c^2 = a^2 + b^2 - 2ab\cos C$$
This is a generalization of the Pythagorean theorem! When $C = 90°$, it reduces to $c^2 = a^2 + b^2$.
3. Angle Sum Property
$$A + B + C = 180°$$
If you know two angles, you can always find the third!
Interactive Triangle Explorer
Drag the vertices to change the triangle. Watch how sides and angles update in real time!
Interactive visualization — available in the full lesson