Triangle Calculator

For right triangles: a^2 + b^2 = c^2, where c is the hypotenuse (longest side, opposite the right angle). If a=3, b=4, then c = sqrt(9+16) = sqrt(25) = 5. This is the most famous equation in geometry and is used throughout engineering and architecture.

Three methods: (1) Base x Height / 2 (if you know base and perpendicular height). (2) Heron formula: s=(a+b+c)/2, Area=sqrt(s(s-a)(s-b)(s-c)) (if you know all 3 sides). (3) (1/2) x a x b x sin(C) (if you know 2 sides and included angle).

These are ways to specify a triangle: SSS=three sides, SAS=two sides and included angle, ASA=two angles and included side, AAS=two angles and non-included side, SSA=two sides and non-included angle (may have ambiguous case). All except SSA uniquely determine a triangle.

By sides: Equilateral (all 3 sides equal), Isosceles (2 sides equal), Scalene (no sides equal). By angles: Acute (all angles < 90deg), Right (one angle = 90deg), Obtuse (one angle > 90deg). An equilateral triangle is always acute. A right triangle can be scalene or isosceles.

c^2 = a^2 + b^2 - 2ab*cos(C). It generalizes the Pythagorean theorem to any triangle. When angle C = 90deg, cos(C) = 0 and it reduces to c^2 = a^2 + b^2. Use it when you know SSS or SAS and need to find unknown sides or angles.