Enter any two known sides (two legs, or one leg and the hypotenuse) to find the missing side, both acute angles, and the area.
Fill in exactly two values, leave the unknown one blank.
This tool calculates missing sides, angles, area, and perimeter of a right triangle (a triangle with one 90-degree angle) based on any two known values. It combines the Pythagorean theorem with basic trigonometric functions for a complete solution.
Pythagorean theorem: a² + b² = c² (where c is the hypotenuse). Trigonometric ratios: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent. Area = ½ × base × height (using the two legs as base and height).
Enter any two known values (two sides, or one side and one angle), and the calculator solves for all remaining sides, angles, area, and perimeter.
Example: A right triangle with legs 6 and 8 has a hypotenuse of √(6² + 8²) = 10, an area of ½ × 6 × 8 = 24 square units, and the non-right angles can be found using inverse trigonometric functions.
What makes a triangle a "right" triangle? A right triangle has exactly one 90-degree (right) angle, which is what allows the Pythagorean theorem and basic trigonometric ratios to apply directly.
How do I find an angle if I only know the side lengths? Use inverse trigonometric functions — for example, if you know the opposite and hypotenuse, angle = arcsin(opposite/hypotenuse).
What's the difference between this tool and the general triangle calculator? This tool is optimized specifically for right triangles and can solve problems using simpler Pythagorean and trigonometric relationships that don't apply to general (non-right) triangles.
Can a right triangle have two equal sides? Yes, this is called a right isosceles triangle, where the two legs are equal length and the two non-right angles are each 45 degrees.
Why are 3-4-5 and similar ratios important? These are Pythagorean triples — sets of whole numbers that satisfy the Pythagorean theorem exactly, making them convenient reference values for checking right angles without complex calculations.