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Triangle Calculator
Solve for all sides, angles, area, perimeter, and heights of any triangle. Select your known inputs below to get started.
Input Triangle Data
Results
| Metric | Solution 1 |
|---|---|
| Side a | — |
| Side b | — |
| Side c | — |
| Angle A | — |
| Angle B | — |
| Angle C | — |
| Area | — |
| Perimeter | — |
| Heights (h_a, h_b, h_c) | — |
| Triangle Type | — |
Solving Triangles
Solving a triangle means finding all its missing sides and angles. Every triangle has six main parts: three sides ($a$, $b$, $c$) and three angles ($A$, $B$, $C$). If you know any three of these values (with at least one of them being a side), you can determine the other three.
Law of Sines
The Law of Sines describes the ratio relationship between side lengths and their opposite angles: $$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$$ It is commonly used when you know AAS, ASA, or the ambiguous SSA case.
Law of Cosines
The Law of Cosines is a generalization of the Pythagorean theorem for any triangle: $$a^2 = b^2 + c^2 - 2bc \cos(A)$$ $$b^2 = a^2 + c^2 - 2ac \cos(B)$$ $$c^2 = a^2 + b^2 - 2ab \cos(C)$$ Use it when you know all three sides (SSS) or two sides and the included angle (SAS).
Ambiguous SSA Case
When given two sides and a non-included angle (SSA), it is possible to find **zero, one, or two valid triangles**. This occurs because the sine function can have the same value for both an acute angle $\theta$ and an obtuse angle $180^\circ - \theta$.