Triangle Calculator

Calculate triangle area, perimeter, and missing sides. Supports multiple calculation methods for any triangle type.

One side of the right angle

Other side of the right angle

Angle between the two sides

Basic Area: A = (Base * Height) / 2\n\nHeron's Formula: A = sqrt[s(s-a)(s-b)(s-c)]\nwhere s = (a+b+c)/2\n\nPythagorean (Right �^3): c^2 = a^2 + b^2\n\nSAS Area: A = (1/2)ab sin(C)\n\nLaw of Cosines: c^2 = a^2 + b^2 - 2ab cos(C)
Example 1 (Right Triangle):\nLeg A = 3, Leg B = 4\n\nHypotenuse = sqrt(9 + 16) = 5\nArea = (3 * 4) / 2 = 6\nPerimeter = 3 + 4 + 5 = 12\n\nExample 2 (Heron's):\nSides: 7, 8, 9\ns = (7+8+9)/2 = 12\nArea = sqrt[12*5*4*3] = sqrt720 = 26.83

What are the basic formulas for triangles?

Area = (Base * Height) / 2 for any triangle. Perimeter = Side A + Side B + Side C. For right triangles: Pythagorean Theorem a^2 + b^2 = c^2. Triangle angle sum = 180deg. These formulas work for all triangle types.

How do I find missing sides and angles?

Use Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) for any triangle. Law of Cosines: c^2 = a^2 + b^2 - 2ab*cos(C) when you know two sides and included angle. Need at least 3 pieces of information to solve a triangle.

What is the difference between triangle types?

Right triangle: one 90deg angle, uses Pythagorean theorem. Equilateral: all sides equal, all angles 60deg. Isosceles: two sides equal. Scalene: all sides different. Acute: all angles < 90deg. Obtuse: one angle > 90deg.

Can any three numbers form a triangle?

No. Triangle Inequality Theorem: sum of any two sides must be greater than the third side. For sides a, b, c: a+b > c AND b+c > a AND a+c > b. If any fails, the sides cannot form a triangle.

How do I calculate area without height?

If you know all three sides, use Heron's formula: s = (a+b+c)/2, then Area = sqrt[s(s-a)(s-b)(s-c)]. If you know two sides and the included angle: Area = (1/2)ab*sin(C). These work without knowing the height directly.