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Study & learning

Triangle Solver

Find every missing side and angle of a triangle, with a drawing.

Private by design

Your inputs stay on your device and are not sent to our servers. Optional usage analytics does not receive your files or tool inputs.

Preparing tool

How to use Triangle Solver

Fill in any three values: sides a, b, c (opposite angles A, B, C) and angles in degrees. Leave the rest blank.
Read the missing sides and angles, the area, and the drawing. If two triangles fit, both are shown.
Follow the working, then copy it or share a link.

Read the detailed guide →

What are the limits of Triangle Solver?

Needs exactly three values including at least one side; three angles alone cannot fix the size. Plane (flat) triangles only, angles in degrees. The drawing is to scale but not a measured diagram. Nothing you enter leaves your device.

Triangle Solver

Sine rule, cosine rule and the ambiguous case

Sides (any units)

Side a

Side b

Side c

Angles (degrees)

Angle A (°, opposite a)

Angle B (°, opposite b)

Angle C (°, opposite c)

Triangle 1: Sides a · b · c6 · 10 · 11.9769

Triangle 1: Angles A · B · C30° · 56.4427° · 93.5573°

Triangle 1: Area29.9422perimeter 27.9769

Triangle 2: Sides a · b · c6 · 10 · 5.3436

Triangle 2: Angles A · B · C30° · 123.5573° · 26.4427°

Triangle 2: Area13.3591perimeter 21.3436

Triangle 1 · scalene, obtuse

Triangle 2 · scalene, obtuse

How it works

Side a is opposite angle A, b opposite B and c opposite C. The sine rule (a ÷ sin A = b ÷ sin B = c ÷ sin C) and the cosine rule (a² = b² + c² − 2bc cos A) link them, so any three values that fix the triangle give the rest.

Method: SSA
Two different triangles fit these values (the ambiguous case).

— Triangle 1 —
Two sides and an angle not between them given (SSA): the sine rule may give two triangles. sin B = b × sin A ÷ a = 10 × sin 30° ÷ 6 = 0.8333.
First solution (acute): B = 56.4427°. Third angle C = 180° − 30° − 56.4427° = 93.5573°.
Sine rule: c = a × sin C ÷ sin A = 6 × sin 93.5573° ÷ sin 30° = 11.9769.
Area = ½ × b × c × sin A = ½ × 10 × 11.9769 × sin 30° = 29.9422. Perimeter = 6 + 10 + 11.9769 = 27.9769.
— Triangle 2 —
Two sides and an angle not between them given (SSA): the sine rule may give two triangles. sin B = b × sin A ÷ a = 10 × sin 30° ÷ 6 = 0.8333.
Second solution (obtuse, 180° − first): B = 123.5573°. Third angle C = 180° − 30° − 123.5573° = 26.4427°.
Sine rule: c = a × sin C ÷ sin A = 6 × sin 26.4427° ÷ sin 30° = 5.3436.
Area = ½ × b × c × sin A = ½ × 10 × 5.3436 × sin 30° = 13.3591. Perimeter = 6 + 10 + 5.3436 = 21.3436.

Enter exactly three values; leave the other boxes empty.
SSA (two sides and an angle not between them) can give two triangles, one, or none.
Angles are in degrees and always add up to 180°.

SSS and SAS use the cosine rule; ASA and AAS use the angle sum and the sine rule; SSA uses the sine rule and checks both the acute and the obtuse angle. Area = ½bc sin A. Computed in double precision and shown to 4 decimal places.