Right Triangle Calculator

Fast, accurate, and free online Right Triangle Calculator tool that runs directly in your browser.

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2

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                                                function runTool() {

                                                  return "Result ready in 0.1s";

                                                }

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Right triangle calculator - Pythagorean theorem and trigonometry

A right triangle (90° angle) is the foundation of geometry and trigonometry. The calculator calculates all sides, angles, area and perimeter based on any two known values - just enter 2 of the 5 parameters (a, b, c, α, β) and everything is ready.

right triangle calculator Pythagorean theorem calculator calculate the sides of a triangle trigonometry calculator

Pythagorean theorem

a² + b² = c² (where c is the hypotenuse). Determination: c = √(a²+b²). a = √(c²-b²). b = √(c²-a²). Example: a=3, b=4 → c=5 (Pythagorean triple 3-4-5). Pythagorean triples: 5-12-13, 8-15-17, 7-24-25, 20-21-29.

Trigonometric functions

sin(α) = a/c (opposite/hypotenuse). cos(α) = b/c (adjacent/hypotenuse). tan(α) = a/b (opposite/adjacent). Determining the angle: α = arcsin(a/c) = arccos(b/c) = arctan(a/b). Sum of angles: α + β = 90° (angle at C always 90°).

Area and perimeter

Area = (a × b) / 2. Perimeter = a + b + c. Radius of the inscribed circle (r): r = (a + b - c) / 2. Radius of the inscribed circle (R): R = c / 2 (the inscribed circle has its center at half of the hypotenuse).

Calculations with different input data

Data a and b: c=√(a²+b²), α=arctan(a/b), β=arctan(b/a). Given c and α: a=c×sin(α), b=c×cos(α), β=90°-α. Given a and α: c=a/sin(α), b=a/tan(α), β=90°-α. Given a and c: b=√(c²-a²), α=arcsin(a/c), β=arcsin(b/c). The tool supports any combination.

FAQ

What is the Pythagorean Trinity?

The Pythagorean trinity is 3 integers (a, b, c) satisfying a²+b²=c². Original three: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Generation: a=m²-n², b=2mn, c=m²+n² for m>n>0. Euclid's formulas for all primary Pythagorean triples.

How to remember trigonometric functions?

SOH-CAH-TOA mnemonic (English): Sin=Opposite/Hypotenuse, Cos=Adjacent/Hypotenuse, Tan=Opposite/Adjacent. In Polish: "Sine is Opposite over Hypotenuse". Alternative: imagine a triangle with the sides labeled.

What are the uses of a right triangle?

Construction: calculation of roof slope (angle + length). Navigation: distance and direction. Physics: distribution of forces (vectors). Electronics: impedance in AC circuits. Computer graphics: 2D/3D transformations. Geodesy: triangulation of terrain points.

How to calculate a right triangle on a scientific calculator?

Sin/cos/tan key: enter the angle, result = ratio of the sides. Arcsin/arccos/arctan key (2nd + sin): enter the ratio, result = angle in degrees. DEG/RAD switch: Use DEG for common tasks. The online tool automatically calculates all values at once.

What is Pythagorean triple and how to check it?

Check: a²+b²=c²? For 6-8-10: 36+64=100 ✓. For 5-7-9: 25+49=74≠81 ✗. Every multiple of a Pythagorean triple is also a three: 3-4-5 → 6-8-10 → 9-12-15.

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