Right Triangle Calculator
Select two known values (sides or angles) and enter them below to solve the complete triangle. The right angle C = 90° is always known.
How the Calculation Works
A right triangle has legs $a$ and $b$ and hypotenuse $c$, with the right angle at $C = 90°$ and acute angles $A$ and $B$ where $A + B = 90°$.
Formulas Used
Pythagorean Theorem:
$$c = \sqrt{a^2 + b^2}$$Trigonometric relationships:
$$\sin A = \frac{a}{c}, \quad \cos A = \frac{b}{c}, \quad \tan A = \frac{a}{b}$$Angle sum:
$$A + B = 90°$$For non-right triangles, use the Law of Sines calculator or the Law of Cosines calculator.
Frequently Asked Questions
What counts as a valid right triangle?
All sides must be positive. Angle A must be strictly between 0° and 90° (the right angle is already at C). If the hypotenuse is shorter than either leg, the triangle is impossible — the calculator will tell you.
Why can't I enter two angles?
Knowing two angles (one of which is 90°) determines the third angle, but gives you no size information. You need at least one side to uniquely solve the triangle. The shape is defined by angles, but scale requires a side.
What's the difference between a leg and a hypotenuse?
The two legs (a and b) form the right angle. The hypotenuse (c) is opposite the right angle and is always the longest side of a right triangle.
