Every side, angle and the area — from three sides or two and an angle.
Area
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Sides a, b, c
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Angles A, B, C
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Perimeter
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Type
Drawn to scale
How this works
Pythagoras c² = a² + b² (right triangles only)
Law of cosines c² = a² + b² − 2ab·cos(C) (any triangle)
Heron's area s = (a+b+c)/2, A = √(s(s−a)(s−b)(s−c))
Area from SAS A = ½·a·b·sin(C)
Given
Use
Three sides
Law of cosines for angles, Heron for area
Two sides and the angle between
Law of cosines for the third side
Two legs of a right triangle
Pythagoras
Any two of a right triangle
Pythagoras, rearranged
Three sides only form a triangle if each pair adds to more than the third — the triangle inequality.
The angles always total 180°.
3-4-5 is the smallest whole-number right triangle, which is why builders use it to square a corner.
How do I find the hypotenuse?
Square both shorter sides, add them, take the square root. For legs of 3 and 4: √(9 + 16) = 5.
How do I find the area without the height?
With all three sides use Heron's formula. With two sides and the angle between them, the area is ½·a·b·sin(C).
Why does it say my sides cannot form a triangle?
Because two of them together are shorter than the third — sides of 1, 2 and 10 can never meet. Each pair must add to more than the remaining side.
How do I calculate the sides of a triangle?
It depends what you already know. With all three sides, the calculator finds every angle. With two sides and the angle between them, it finds the third side with the law of cosines. With two sides of a right triangle, it finds the missing one with Pythagoras. Pick the matching tab above and enter what you have.