Triangle calculator
Enter any three values (at least one side) and get every side, angle, the area, perimeter and a drawing to scale. Handles the ambiguous SSA case.
Law of cosines for two angles, then C = 180° − A − B.
The laws behind the solver
Law of sines: a / sin A = b / sin B = c / sin C. Each side is proportional to the sine of the angle opposite it.
Law of cosines: c² = a² + b² − 2ab·cos C. It is the Pythagorean theorem with a correction term; when C = 90°, cos C = 0 and it reduces to c² = a² + b².
Angle sum: A + B + C = 180°, in every flat triangle.
For right triangles, the right triangle calculator needs only two values and covers 30-60-90 and 45-45-90 triangles.
Show me the steps
An AI tutor walks through the working for this exact result. The answer above is computed in your browser; the explanation is optional and is the only thing that leaves your device.
Solve the SSS triangle with a = 7, b = 8, c = 9 (angles in degrees) = a=7, b=8, c=9, A=48.189685°, B=58.411864°, C=73.39845°
Questions people ask
What do SSS, SAS, ASA, AAS and SSA mean?
They list which parts you know, in order around the triangle: S for a side, A for an angle. SAS means two sides and the angle between them; AAS means two angles and a side that is not between them. Any of these (with at least one side) fixes the triangle, except SSA, which can give two answers.
What is the ambiguous case?
With two sides and an angle not between them (SSA), the unknown side can swing to two positions. If a is shorter than b but longer than b·sin A, two different triangles fit. The calculator shows both.
When do I use the law of sines vs the law of cosines?
Use the law of cosines (c² = a² + b² − 2ab cos C) when you know three sides or two sides and the included angle. Use the law of sines (a/sin A = b/sin B = c/sin C) when you know an angle and its opposite side.
How is the area calculated?
With Heron’s formula: s = (a + b + c)/2, area = √(s(s − a)(s − b)(s − c)). It needs only the three sides, which the solver always finds.
How do I find the 3 sides of a triangle?
You need three known values including at least one side. With three angles only, the size is unknown. With two sides and the included angle (SAS), the law of cosines gives the third side; with two angles and a side (ASA/AAS), the law of sines gives the other two.
What is the 45-45-90 rule?
A right triangle with two 45° angles has equal legs, and its hypotenuse is a leg times √2. The right triangle calculator has a dedicated 30-60-90 and 45-45-90 solver.
What is a median of a triangle?
The line from a vertex to the midpoint of the opposite side. Its length is mₐ = ½√(2b² + 2c² − a²). The three medians meet at the centroid, two thirds of the way along each.
Can I solve a triangle from three angles?
No. Three angles fix the shape but not the size; infinitely many similar triangles share them. You need at least one side length.