Right Triangle Calculator

A right triangle has one 90° angle, so knowing just two other measurements is enough to find everything. This calculator uses SOHCAHTOA and the Pythagorean theorem to find all three sides and both acute angles, from two sides or one side and one angle. It also gives the area and perimeter and draws the triangle.

Try:

How to use the right triangle calculator

  1. Choose what you know, such as both legs or the hypotenuse and an angle.
  2. Enter the values (angles in degrees).
  3. Press Calculate to see every side and angle.

Formula

sin⁡A=ac,  cos⁡A=bc,  tan⁡A=ab\sin A = \frac{a}{c},\; \cos A = \frac{b}{c},\; \tan A = \frac{a}{b}

Worked example: Legs 5 and 12

  • What do you know?: Both legs a and b
  • Leg a (opposite A): 5
  • Leg b (adjacent to A): 12

✓ Answer checked

a=5,  b=12,  c=13,  A≈22.6199∘,  B≈67.3801∘a = 5,\; b = 12,\; c = 13,\; A \approx 22.6199^\circ,\; B \approx 67.3801^\circ
Area
3030
Perimeter
3030
A 22.62°B 67.38°b = 12a = 5c = 13
The right triangle drawn to scale; the square marks the right angle.
Step-by-step working (2 steps)

  1. Use tan and Pythagoras TOA

    tan A = opposite ÷ adjacent, and c² = a² + b².

    tan⁡A=512⇒A≈22.6199∘,c=52+122≈13\tan A = \frac{5}{12} \Rightarrow A \approx 22.6199^\circ,\quad c = \sqrt{5^2 + 12^2} \approx 13

  2. Third angle

    The two acute angles add to 90°.

    B=90∘−22.6199∘=67.3801∘B = 90^\circ - 22.6199^\circ = 67.3801^\circ
Formulas used
sin⁡A=ac,  cos⁡A=bc,  tan⁡A=ab\sin A = \frac{a}{c},\; \cos A = \frac{b}{c},\; \tan A = \frac{a}{b}
a2+b2=c2a^2 + b^2 = c^2
How this was checked
  • ✓ The sides satisfy a² + b² = c², and sin A = a ÷ c.

Frequently asked questions

What does SOHCAHTOA mean?

Sin = Opposite ÷ Hypotenuse, Cos = Adjacent ÷ Hypotenuse, Tan = Opposite ÷ Adjacent.

How tall does a 6 m ladder reach at 70°?

6 × sin 70° ≈ 5.64 m up the wall.

How do I find an angle from two sides?

Use the inverse function. With opposite 5 and adjacent 12, A = tan⁻¹(5/12) ≈ 22.6°.

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