Solve a right triangle from any two facts
A right triangle is fully determined by just two pieces of information beyond the right angle itself. Tell this calculator which two you know — two legs, a leg and the hypotenuse, or a side and an acute angle — and it finds every remaining side and angle, plus the area and perimeter.
The relationships
With the right angle at C, legs a and b, and hypotenuse c: a squared plus b squared equals c squared. The acute angles satisfy sin A = a / c, cos A = b / c, and tan A = a / b, while A plus B equals 90 degrees. Those relationships let any two knowns unlock the rest.
Which two do you have?
| You know | Method |
|---|---|
| Two legs | Pythagoras, then arctangent |
| Leg + hypotenuse | Pythagoras, then arcsine |
| Side + angle | sine, cosine, tangent ratios |
Related tools
For the hypotenuse alone, the Pythagorean theorem calculator; for the raw ratios at any angle, the trig function calculator.
Worked example
Legs of 3 and 4 give a hypotenuse of 5, angle A of about 36.87 degrees, angle B of about 53.13 degrees, an area of 6, and a perimeter of 12.
FAQ
Why only two knowns?
The right angle is the third fact for free. Two more — as long as at least one is a side — pin the triangle down completely.
Can I enter two angles?
Two angles fix only the shape, not the size, so you always need at least one side length to solve a specific triangle.