NumberTally Right Triangle Calculator
Solve any right triangle from just two known values: two sides, or one side plus one acute angle. Get all three sides and both acute angles instantly, with the full working shown, a labeled diagram, and special-triangle detection. Free, no sign-up.
Advanced options
Convention: side a is opposite angle A, side b opposite angle B, hypotenuse c opposite the 90° angle C.
How two values unlock the whole triangle
A right triangle has five unknowns (3 sides, 2 acute angles — the third angle is always 90°). The Pythagorean theorem (a² + b² = c²) and SOH CAH TOA ratios link them, so any two independent values determine the rest: two sides give the third side, then inverse trig gives the angles; a side plus an angle gives everything through sine, cosine, and tangent.
SOH CAH TOA, decoded
Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent — always relative to the angle you're working with. For angle A, the "opposite" side is a and the "adjacent" side is b.
Frequently Asked Questions
What two values does a right triangle solver need?
Any two, as long as at least one is a side: two sides, or one side plus one acute angle. Two angles alone aren't enough — they'd describe the shape but not the size.
How do you find the angles of a right triangle?
Use inverse trig: angle A = arctan(a/b), or arcsin(a/c), or arccos(b/c). The other acute angle is just 90° minus the first.
What is SOH CAH TOA?
A mnemonic for the trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. Pick the ratio containing your knowns.
Do the two acute angles always add up to 90 degrees?
Yes — all three angles sum to 180°, and the right angle takes 90°, leaving exactly 90° for A + B.
What are the 30-60-90 and 45-45-90 special triangles?
Triangles with exact side ratios: 30-60-90 has sides 1 : √3 : 2; 45-45-90 (isosceles right) has 1 : 1 : √2. The calculator flags when your triangle matches one.