Pythagorean Theorem & Right Triangle Calculator
Solve missing sides ($a^2 + b^2 = c^2$), verify primitive Pythagorean triples, evaluate converse acute/obtuse classifications, and calculate exact radical forms
First perpendicular leg
Second perpendicular leg
Calculated Hypotenuse (c)
c = 5.000 cm
Exact Integer Result
Pythagorean Equation: 3.00² + 4.00² = 9.00 + 16.00 = 25.00 = 5.00²
Exact Radical Form
√25 = 5
Square-free reduced form
Acute Angles (∠A, ∠B)
36.87°, 53.13°
0.6435 rad, 0.9273 rad
Enclosed Area (½ · a · b)
6.000 cm²
Perimeter: 12.000 cm
Altitude to Hypotenuse (h_c)
2.400 cm
h_c = (a · b) / c
Euclid’s Formula Generator (m > n > 0)
Greater integer (m > n)
Lesser integer
k=1: Primitive Triple
Generated Pythagorean Triple (a, b, c)
(3, 4, 5)
Primitive Pythagorean Triple (gcd = 1)
a = k(m² – n²) = 3 • b = k(2mn) = 4 • c = k(m² + n²) = 5
Equation Sum Check
3² + 4² = 5²
9 + 16 = 25 (Identity Verified)
Inradius (r = (a + b – c) / 2)
1.000
r = n(m – n) integer property
Parity & Coprime Nature
Coprime & Opposite Parity
gcd(2, 1) = 1 • m, n not both odd
Area & Perimeter
Area: 6 • P: 12
Always divisible by 6 & 12
Three Side Lengths (Any Order)
Converse Geometric Classification
Obtuse Triangle (c² > a² + b²)
Obtuse Scalene (Widest Angle > 90°)
9.00² = 81.00 > 5.00² + 7.00² = 74.00 (Δ = +7.000)
Pythagorean Difference (c² – (a² + b²))
+7.000
> 0 implies angle > 90°
Maximum Interior Angle (∠C)
95.74°
Law of Cosines evaluation
Other Interior Angles
33.56°, 50.70°
Sum of interior angles = 180°
Triangle Inequality Check
Valid (5 + 7 > 9)
Sum of 2 shorter sides exceeds longest