Triangle Solver

Enter three known parts of any triangle (at least one side) to find the missing sides and angles, area and perimeter.

What Do You Know?
Fractions and decimals both work.
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Area
Sides
Angles
Area
Perimeter
Type
Second solution
Method

Saved Calculations

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How to Solve Any Triangle

Side a is opposite angle A, b opposite B, and c opposite C. The angles always add up to 180°.

Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C
Law of cosines: a² = b² + c² − 2bc cos A
Area = ½ ab sin C = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2

Use the law of cosines when you know three sides (SSS) or two sides and the angle between them (SAS). Use the law of sines when you know two angles (ASA, AAS). SSA can have zero, one or two answers, which is why it’s called the ambiguous case.

Worked Example

Tips

Three angles alone (AAA) don’t fix a triangle’s size, only its shape, so at least one side is always needed. For right triangles, the right triangle calculator is quicker.