RIGHT TRIANGLE
Right triangles, the theorem does the rest.
Fill any two of a, b (the legs) and c (the hypotenuse, always opposite the right angle and the longest side); we compute the third side, the three angles, area and perimeter. There are also 30°-60°-90° and 45°-45°-90° shortcuts and random practice.
Side ratios: 30-60-90 is 1 : √3 : 2; 45-45-90 is 1 : 1 : √2. Click to fill by ratio (edit the shortest side to scale).
Everything runs locally in your browser
How to use
Fill any two of a / b / c (legs a, b vs hypotenuse c — the hypotenuse is opposite the right angle and always longest), tap solve to get the third side, the three angles, area and perimeter. If c is shorter than the other leg you get a "no right triangle" warning. Special-triangle buttons fill by ratio; change the shortest side to scale. Practice gives a random Pythagorean triple to compute mentally.
常见问题
How do I tell the leg from the hypotenuse?
The side opposite the 90° angle is the hypotenuse and is always the longest; the other two (the "legs") meet at the right angle. Here a, b are legs and c is the hypotenuse, so c is always ≥ a, b.
How is Pythagoras related to the law of cosines?
The theorem is the law of cosines at a right angle (C=90°, cos90°=0): c² = a² + b² − 2ab·cosC collapses to c² = a² + b². So this tool is for right triangles only; arbitrary triangles need the full law of cosines.
Why is 30-60-90 equal to 1:√3:2?
Split an equilateral triangle by its height into two 30-60-90 triangles: short leg (half the side) : long leg (the height, √3/2 by Pythagoras) : hypotenuse (original side) = 1 : √3 : 2. A 45-45-90 is an isosceles right triangle, legs equal, hypotenuse = leg × √2.
Is any data uploaded?
No. All solving runs locally in the browser.