# Triangle Solver - Law of Sines and Law of Cosines Calculator

> Free online triangle solver: SSS, SAS, ASA, AAS and SSA inputs give every side and angle plus the area, perimeter, heights, circumradius and inradius.

- URL: https://qilingtools.com/en/math/triangle
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Give any three elements of a triangle (including at least one side) and the rest are solved for you: all three sides and angles, area, perimeter, the three heights, circumradius R and inradius r, plus whether the triangle is acute, right or obtuse.

## How to use

1. Choose what you know: SSS, SAS, ASA, AAS or SSA
2. Enter the three known values (angles in degrees)
3. Read every side, angle and derived quantity

## Features

- Five input cases: SSS / SAS / ASA / AAS / SSA
- Law of cosines or sines picked automatically, obtuse angles handled correctly
- Area, perimeter, three heights, circumradius and inradius
- Classifies acute/right/obtuse and equilateral/isosceles/scalene
- Warns about the second SSA solution

## FAQ

### How do I find the angles from three sides?

By the law of cosines: cos A = (b²+c²−a²)/(2bc), then take the inverse cosine. Choose SSS and all three angles are computed.

### Why can SSA have two solutions?

With two sides and a non-included angle the unknown angle can be acute or its obtuse supplement — the “ambiguous case”. The tool reports the alternative value of B when one exists.

### How do I know three lengths form a triangle?

Each pair must sum to more than the third side; otherwise the tool says no triangle exists.

### How is the circumradius calculated?

R = abc / (4·Area), and the inradius is r = Area / s with s the semi-perimeter. Both are shown.

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