📐 Triangle Calculator

Base & Height: Area = (1/2) × base × height
Heron's Formula: s = (a+b+c)/2
Area = √(s(s-a)(s-b)(s-c))
SAS: Area = (1/2) × a × b × sin(C)
Equilateral: Area = (√3/4) × a²

a² + b² = c² (right triangle only)

Finding hypotenuse: c = √(a² + b²)
Finding leg: a = √(c² - b²)

Pythagorean triples: 3-4-5, 5-12-13,
8-15-17, 7-24-25, 20-21-29

c² = a² + b² - 2ab·cos(C)
b² = a² + c² - 2ac·cos(B)
a² = b² + c² - 2bc·cos(A)

Finding angle: cos(C) = (a² + b² - c²) / (2ab)

a/sin(A) = b/sin(B) = c/sin(C)

Finding side: a = b × sin(A) / sin(B)
Finding angle: sin(A) = a × sin(B) / b

Also equals 2R (where R = circumradius)

Perimeter: P = a + b + c
Semi-perim: s = P/2
Inradius: r = Area / s
Circumradius: R = (abc) / (4 × Area)
Height (ha): ha = 2×Area / a
Median (ma): ma = (1/2)√(2b²+2c²-a²)

Interior angles: A + B + C = 180°
Exterior angle = sum of 2 non-adjacent interior angles

Right triangle: A + B = 90° (complementary angles)
sin(A) = cos(B), cos(A) = sin(B), tan(A) = a/b