Right Triangle Calculator

Find hypotenuse, sides, angles, and area of any right triangle using Pythagoras and trig.

Right Triangle (SOH-CAH-TOA)

sin A = a/c   cos A = b/c   tan A = a/b

a² + b² = c² (Pythagoras)

Leg a (opp A)

3

Leg b (adj A)

4

Hypotenuse c

5

Angle A

36.8699°

Angle B

53.1301°

Angle C

90°

Area

6

Perimeter

12

sin A = 0.6   cos A = 0.8   tan A = 0.75

Right Triangle Calculator Formula & How It Works

c² = a² + b² | sin θ = opp/hyp | cos θ = adj/hyp | tan θ = opp/adj
  • c = hypotenuse (side opposite the right angle)
  • a, b = legs (sides forming the right angle)
  • θ = one of the acute angles
  • Angles sum to 180°; right angle = 90°

A right triangle has one 90° angle. The Pythagorean theorem gives the hypotenuse from the two legs. Trigonometric ratios (SOH-CAH-TOA) relate sides to angles. Inverse trig (sin⁻¹, cos⁻¹, tan⁻¹) finds angles from sides. Special right triangles: 3-4-5, 5-12-13, 30-60-90, 45-45-90.

Right Triangle Calculator FAQs

What is SOH CAH TOA?

A mnemonic for right triangle trig ratios: SOH = Sine = Opposite/Hypotenuse. CAH = Cosine = Adjacent/Hypotenuse. TOA = Tangent = Opposite/Adjacent. For angle θ, 'opposite' is the side across from it; 'adjacent' is the side next to it (not hypotenuse).

What are Pythagorean triples?

Sets of three whole numbers satisfying a²+b²=c². Common ones: (3,4,5), (5,12,13), (8,15,17), (7,24,25). Any multiple works: (6,8,10), (9,12,15). Pythagorean triples are useful for quick mental geometry checks.

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