256 Tools

Triangle Solver

Enter all three side lengths (a, b, c).

cba
a
3
b
4
c
5
A°
36.87
B°
53.13
C°
90
Area
6
Perimeter
12

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Solve a triangle from what you know: three sides (SSS), two sides and the angle between them (SAS), or two angles and the side between them (ASA). It finds all remaining sides and angles plus the area and perimeter, and draws the triangle. Everything runs in your browser.

How to use

  1. Pick which values you know: 3 sides, 2 sides + angle, or 2 angles + side.
  2. Enter the values (angles in degrees).
  3. Read the full set of sides, angles, area and perimeter.

How it works

Each side is opposite the angle with the same letter (side a faces angle A). With three sides, the law of cosines gives each angle. With two sides and the included angle, the law of cosines finds the third side. With two angles and a side, the third angle is 180 minus the other two, and the law of sines gives the remaining sides. The area uses Heron's formula.

A triangle labelled with sides a, b, c and angles A, B, C.cbaABC

Features

Three input modes

Solve from SSS, SAS or ASA — the common ways a triangle is defined.

Area & perimeter

Get the area (Heron's formula) and perimeter along with the angles.

Validity check

Impossible triangles are detected and flagged instead of giving wrong numbers.

Diagram

A labelled triangle helps you match sides and angles.

When to use it

Math homework

Check trigonometry answers for triangle problems.

DIY & woodworking

Work out an unknown length or angle for a cut or layout.

Measuring

Find a distance or angle that is hard to measure directly.

Learning

See the law of sines and cosines applied step by step.

Notes

  • Side a is opposite angle A, b opposite B, c opposite C.
  • Angles are entered and shown in degrees.
  • SSA is not supported because it can be ambiguous (two possible triangles).
  • Everything runs on your device; nothing is uploaded.

FAQ

What does SSS mean?
SSS means you know all three sides. From those, the law of cosines determines all three angles.
How do sides and angles relate?
Each side is opposite the angle with the matching letter: side a is across from angle A, and so on.
How is the area found?
It uses Heron's formula, which gives the area from the three side lengths once they are known.
Why won't my triangle solve?
The values may break the triangle inequality (one side longer than the other two combined) or the angles may not be valid. Check the inputs.
Is my data sent to a server?
No. All calculation happens locally in your browser.

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