Right Triangle Calculator
A right triangle needs only two values. Give any two sides, or one side and an acute angle, and get the rest: sides, angles, area, perimeter and height.
- c = √(a² + b²) = √(9 + 16) = √25 = 5
- A = arctan(a ÷ b) = 36.87°, B = 90° − A = 53.13°
- Leg a
- 3
- Leg b
- 4
- Hypotenuse c
- 5
- Angles A · B
- 36.87° · 53.13°
- Area
- 6
- Perimeter
- 12
- Height to c
- 2.4
Solving a right triangle
With two sides, use the Pythagorean theorem for the third. With a side and an angle, use SOH-CAH-TOA:
- sin A = opposite ÷ hypotenuse = a ÷ c
- cos A = adjacent ÷ hypotenuse = b ÷ c
- tan A = opposite ÷ adjacent = a ÷ b
The two acute angles always add to 90°, so once you have one you have both.
Special right triangles
| Triangle | Side ratio | Where you see it |
|---|---|---|
| 45°-45°-90° | 1 : 1 : √2 | Half of a square, cut on the diagonal |
| 30°-60°-90° | 1 : √3 : 2 | Half of an equilateral triangle |
| 3-4-5 | 3 : 4 : 5 | Builders use it to check a corner is square |
Questions people ask
What is the hypotenuse?
The side opposite the right angle. It is always the longest side.
How do I find an angle from two sides?
Use the inverse trig functions: A = arctan(a ÷ b), or arcsin(a ÷ c), or arccos(b ÷ c).
How do I check a corner is square with a tape measure?
Mark 3 ft along one wall and 4 ft along the other. If the diagonal between the marks is exactly 5 ft, the corner is 90°. Use 6-8-10 or 9-12-15 for bigger layouts.
Stuck on a word problem?
Paste a homework question or describe your project. The AI tutor names the formula and works it through step by step. Always check the result with the calculator above.