Trig Triangle Solver

Enter any 3 known values (sides and/or angles). Auto-detects the case (SSS, SAS, ASA, AAS, SSA) and solves the complete triangle.

Enter Known Values

Side a is opposite angle A, side b opposite angle B, side c opposite angle C. Leave unknowns blank. Enter angles in degrees.

Solution

Triangle
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Step-by-Step Solution

Triangle Solving Cases

Any triangle can be solved if you know at least 3 values with at least one being a side. The calculator automatically detects which case applies and uses the appropriate method.

The Five Cases

SSS (Side-Side-Side)

All three sides known. Use Law of Cosines to find all angles.

cos(A) = (b^2+c^2-a^2)/(2bc)

SAS (Side-Angle-Side)

Two sides and the included angle. Use Law of Cosines then Law of Sines.

c^2 = a^2+b^2-2ab*cos(C)

ASA (Angle-Side-Angle)

Two angles and the included side. Find third angle, then Law of Sines.

a/sin(A) = b/sin(B) = c/sin(C)

AAS (Angle-Angle-Side)

Two angles and a non-included side. Same as ASA after finding the third angle.

Third angle = 180 - A - B

SSA (Ambiguous Case)

Two sides and a non-included angle. May have 0, 1, or 2 solutions.

sin(B) = b*sin(A)/a

The Ambiguous Case (SSA)

When you know two sides and the angle opposite one of them, the triangle may not be unique. If the sine of the unknown angle exceeds 1, no triangle exists. If both the angle and its supplement (180 minus the angle) produce valid triangles, two solutions exist. This calculator handles all possibilities and shows all valid solutions.

Validation Checks

  • All sides must be positive numbers.
  • All angles must be between 0 and 180 degrees.
  • The sum of any two sides must exceed the third side (triangle inequality).
  • The sum of all angles must equal 180 degrees.