Enter any two known values of a right triangle (legs a and b, hypotenuse c, or an acute angle) to find all remaining sides, angles, area, altitude, and whether the triangle forms a Pythagorean triple.
How to use this calculator
Choose which two values you know: two legs, hypotenuse + one leg, one leg + acute angle, or hypotenuse + acute angle.
Enter those two values in the fields shown.
Read hypotenuse, area, perimeter, both acute angles, and altitude to hypotenuse instantly.
The calculator also checks whether your triangle forms a Pythagorean triple (integer sides).
Formula & method
Pythagorean Theorem & Trigonometry
c = √(a² + b²) · Area = ½ab · sin A = a/c · cos A = b/c · tan A = a/b
Right angle C = 90° always. Angles A + B = 90°. Altitude to hypotenuse h = ab / c.
Example
Legs a = 3, b = 4 → c = √(9 + 16) = 5, Area = ½ × 3 × 4 = 6, Angle A = arcsin(3/5) = 36.87°.
Key insights
The Pythagorean theorem a² + b² = c² defines every right triangle uniquely once any two sides are known.
Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25.
The altitude to the hypotenuse h = ab / c creates two smaller right triangles similar to the original.
Sine, cosine, and tangent are defined from the right triangle: sin A = opposite / hypotenuse = a / c.
How to interpret your result
Hypotenuse (c)
The longest side, opposite the 90° angle. Always computed as c = √(a² + b²).
Altitude to hypotenuse (h)
The perpendicular segment from the right angle to the hypotenuse: h = ab / c.
Pythagorean triple
If all three sides are positive integers with a² + b² = c², the triangle is a Pythagorean triple — fundamental in surveying and carpentry.
Frequently asked questions
What is the Pythagorean theorem?
In any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b².
How is this different from the Triangle Calculator?
This tool specializes in right triangles and adds hypotenuse computation, Pythagorean triple detection, and altitude. The Triangle Calculator handles all triangle types.
What is a Pythagorean triple?
A set of three positive integers a, b, c satisfying a² + b² = c². The simplest is 3-4-5; others include 5-12-13 and 8-15-17.
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