BYTETOOLS

Triangle Solver

Solve any triangle from known sides and angles (SSS, SAS, ASA, AAS, SSA) using the laws of sines and cosines. Get all sides, angles, area and perimeter.

3
Side a
4
Side b
5
Side c
36.8699°
Angle A
53.1301°
Angle B
90°
Angle C
6
Area
12
Perimeter
  • Solves SSS, SAS, ASA, AAS and SSA cases
  • Uses the laws of sines and cosines
  • Outputs all sides, angles, area and perimeter
  • Detects and explains impossible triangles
  • Flags the ambiguous SSA case
  • Private, browser-based trigonometry

How to use the Triangle Solver

  1. 1

    Select which parts you know: SSS, SAS, ASA/AAS or SSA.

  2. 2

    Enter the three required values in the labelled fields.

  3. 3

    Read all sides and angles, computed with the laws of sines and cosines.

  4. 4

    Check the area and perimeter shown below the results.

  5. 5

    Watch for notes on the ambiguous SSA case or impossible triangles.

About the Triangle Solver

The ByteTools Triangle Solver finds every unknown side and angle of a triangle from the parts you already know. Choose your case — three sides (SSS), two sides and the included angle (SAS), two angles and a side (ASA/AAS), or two sides and a non-included angle (SSA) — and it applies the law of sines or cosines to solve the rest.

It returns all three sides, all three angles in degrees, plus the area and perimeter, so it is ideal for trigonometry homework, surveying, construction and engineering checks. Impossible triangles, such as sides that break the triangle inequality, are caught and explained rather than returning a wrong answer.

Every calculation runs locally in your browser with JavaScript. Nothing you enter is uploaded or stored, so you can solve triangles quickly and privately.

Frequently asked questions

What information do I need to solve a triangle?

You need three pieces of information that include at least one side. Common cases are three sides (SSS), two sides and the included angle (SAS), two angles and a side (ASA or AAS), or two sides and a non-included angle (SSA).

When do you use the law of cosines versus the law of sines?

The law of cosines suits SSS and SAS, where you know sides around an angle. The law of sines suits ASA, AAS and SSA, where a side pairs with its opposite angle. The solver picks the right law for your case automatically.

What is the ambiguous SSA case?

With two sides and a non-included angle, zero, one or two valid triangles can exist. The solver computes the primary solution and, when a second triangle is also possible, adds a note showing the alternative angle so you are aware of it.

Why does it say my triangle is impossible?

A triangle is impossible if the sides violate the triangle inequality — one side longer than the sum of the other two — or if the angles would exceed 180°. In those cases the solver shows a clear message instead of an invalid result.

How is the area of the triangle calculated?

Once two sides and their included angle are known, the area is one-half times the two sides times the sine of the angle between them. The solver derives the needed values first, then applies this formula to report the area.

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