Triangle Calculator

Solve any triangle — find area, perimeter, angles, and altitudes from known sides/angles.

Triangle Solver

3 Sides

Side a

5

Side b

6

Side c

7

Angle A

44.42°

Angle B

57.12°

Angle C

78.46°

Area

14.6969

Perimeter

18

Height (to a)

5.8788

Acute · Scalene triangle

Triangle Calculator Formula & How It Works

Area = ½ab sin(C) | Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
  • Law of Cosines: c² = a² + b² − 2ab cos(C)
  • Heron's formula: Area = √[s(s-a)(s-b)(s-c)] where s=(a+b+c)/2
  • Sum of angles: A + B + C = 180°
  • Pythagoras: a² + b² = c² (right triangle only)

Any triangle can be fully solved with 3 known measurements (at least one being a side). SSS: use Law of Cosines for angles. SAS: use Law of Cosines for third side, then Law of Sines. ASA/AAS: use angle sum and Law of Sines. The Law of Sines and Cosines are universal tools for any triangle.

Triangle Calculator FAQs

How do you solve a triangle with two sides and the included angle (SAS)?

Step 1: Find third side using Law of Cosines: c² = a² + b² − 2ab cos(C). Step 2: Find another angle using Law of Sines: sin(A)/a = sin(C)/c. Step 3: Third angle = 180° − A − C.

What is the difference between similar and congruent triangles?

Congruent triangles have identical sides and angles (same shape and size). Similar triangles have the same angles but proportional sides (same shape, different size). Congruence conditions: SSS, SAS, ASA, AAS. Similarity conditions: AA, SAS, SSS.

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