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Triangle solver

Enter three of a triangle's sides and angles, at least one side, and see the rest worked out step by step.

Three of the six parts

Sides
Angles

Fill in any three fields, at least one of them a side. Angles in degrees; side a is opposite angle A.

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Solution

Case: Two sides and the angle between them (SAS)

PartValue
Side a7(given)
Side b10(given)
Side c8.888
Angle A43°
Angle B77°
Angle C60°(given)
Area30.311
Perimeter25.888

Working

  1. Law of cosines: c² = a² + b² − 2·a·b·cos C = 7² + 10² − 2·7·10·cos 60°, so c ≈ 8.888
  2. Law of cosines: cos A = (b² + c² − a²) / (2·b·c) = (10² + 8.888² − 7²) / (2·10·8.888), so A ≈ 43°
  3. Angle sum: B = 180° − A − C = 180° − 43° − 60° ≈ 77°
  4. Area rule: Area = a·b·sin C / 2 = 7·10·sin 60° / 2 ≈ 30.311
  5. Perimeter: a + b + c = 7 + 10 + 8.888 ≈ 25.888

The solver takes three of the six parts, works out which case it is (SSS, SAS, ASA, AAS or SSA) and finds the rest with the angle sum, the law of cosines and the law of sines, and the area with the area rule. With two sides and an angle that is not between them there may be two triangles, one or none: with a = 7, b = 10 and A = 30°, B is about 45.58° or 134.42°, and the solver shows both.

Last reviewed October 19, 2026 ·How pages are reviewed

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