Three modes: (1) Right triangle — enter legs a and b to get hypotenuse, area, perimeter and angles via Pythagorean theorem. (2) Any triangle — enter base and height to get area. (3) Three sides — enter all three sides to get area (Heron's formula), perimeter, and all three angles.
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b². Example: a=3, b=4 → c=√(9+16)=5.
Heron's formula computes the area of any triangle knowing only its 3 sides. First compute s = (a+b+c)/2 (semi-perimeter), then Area = √[s(s−a)(s−b)(s−c)].
Formulas: Right triangle: c = √(a²+b²) | Area = ½×a×b | Any triangle (base, height): Area = ½×base×height | 3 sides (Heron's): s=(a+b+c)/2, Area=√[s(s-a)(s-b)(s-c)]
Example (right triangle): a=3, b=4 → c=5 (3-4-5 Pythagorean triple) | Area=6 | Perimeter=12 | Angle A≈36.87° | Angle B≈53.13°.
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