Right Triangle Calculator
| Property | Value |
|---|---|
| Side a | 3 |
| Side b | 4 |
| Hypotenuse c | 5 |
| Angle A | 36.869898° |
| Angle B | 53.130102° |
| Area | 6 |
| Perimeter | 12 |
| Altitude to hypotenuse | 2.4 |
a² + b² = c²
Solving Right Triangles
A right triangle has one 90° angle and two acute angles that sum to 90°. With only two pieces of information (excluding the right angle itself), you can determine all remaining sides and angles using the Pythagorean theorem and basic trigonometry.
Given two sides, apply a² + b² = c² for the missing side, then use sin(A) = a/c, cos(A) = b/c, and tan(A) = a/b to find acute angles. Given one side and one acute angle, use trig ratios to find the remaining sides: opposite = hypotenuse × sin(angle), adjacent = hypotenuse × cos(angle).
Area = (1/2) × leg₁ × leg₂. Perimeter = sum of all three sides. The altitude to the hypotenuse equals (leg₁ × leg₂) / hypotenuse — a useful metric in geometric mean problems.
Two modes are available: "Two sides" (enter any two of a, b, c) and "Side + angle" (specify which side and which acute angle). The diagram updates with labeled sides and a right-angle marker.
This tool is ideal for trigonometry homework, construction layout, navigation problems, and any scenario where a 90° corner is involved.
Examples
| Example | Result |
|---|---|
| Legs 3 and 4 | c=5, A≈36.87°, B≈53.13° |
| Hypotenuse 10, leg 6 | Other leg = 8 |
| Leg 5, angle A=30° | c=10, b≈8.66 |
Frequently asked questions
Enter either acute angle A or B (both less than 90°). The other acute angle is computed as 90° minus the first.
Altitude to hypotenuse = (a × b) / c.
Yes. This tool also finds angles, area, perimeter, and altitude — not just the missing side.