Right Triangle Solver — Sides, Angles, Area
Enter any two known sides or a side and an angle of a right triangle to solve for every side, angle, area.
Side a
3
Side b
4
Hypotenuse c
5
Angle A
36.87°
Angle B
53.13°
Angle C
90°
Area
6
Perimeter
12
Angle C is always 90° by definition. Sides are found with the Pythagorean theorem (a² + b² = c²) and angles with the inverse trig ratios (sine, cosine, tangent) of whichever two values you provide — all four "I know" options solve the same triangle, just starting from different known values.
About this tool
How to use it
- Pick which two values you already know from the 'I know' dropdown — both legs, a leg and the hypotenuse, a leg and angle A, or the hypotenuse and angle A.
- Enter those two values in the fields below (they relabel to match your choice).
- Press Solve Triangle, or just keep typing — every side, angle, area, and perimeter updates live.
- Check the diagram to match the letters (a, b, c, A, B) to the actual sides and angles of your triangle.
Why it matters
A right triangle is fully determined by any two of its measurements besides the right angle itself, but which formula to use — the Pythagorean theorem, or one of sine, cosine, or tangent — depends on which two values you happen to know. Rather than remembering all four formulas, picking what you know from a list and getting every other measurement back removes the formula-selection step entirely.
When to use it
Useful for checking geometry or trigonometry homework, for a quick real-world measurement (like finding a ladder's required length from a wall height and angle, or a roof's rise from its run and pitch angle), or for verifying a triangle you've already partly solved by hand.
Good to know
Angle C is always 90° by definition — a right triangle has exactly one right angle, opposite the hypotenuse. Side a is opposite angle A, and side b is opposite angle B, matching the diagram. All four 'I know' options solve the exact same underlying triangle when given consistent values; they only differ in which two measurements you start from.
Common questions
Which sides and angles do the letters a, b, c, A, B refer to?
Side a is opposite angle A, side b is opposite angle B, and c is always the hypotenuse (the side opposite the right angle, angle C). The diagram above the inputs shows exactly where each one sits on the triangle.
Why do all four options give the same answer for an equivalent triangle?
A right triangle only needs two independent measurements (beyond the fixed 90° angle) to be fully determined — whichever two you start from, the Pythagorean theorem and the trig ratios connect all the others, so a 3-4-5 triangle solved from its two legs is the identical triangle to one solved from a leg and its adjacent angle.
What if I enter a leg that's larger than the hypotenuse?
That's not possible in a real right triangle — the hypotenuse is always the longest side — so the calculator hides the result rather than showing a nonsensical answer when the leg-and-hypotenuse combination has the leg equal to or greater than the hypotenuse.
Can I enter an angle of 90° or more?
No — angle A must be strictly between 0° and 90°, since it's one of the two acute angles in a right triangle (the third angle is always exactly 90°, and the two acute angles always add up to the remaining 90°).