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Pythagorean Theorem & SOHCAHTOA Calculator

Solve any right triangle from two values: missing sides with the Pythagorean theorem and angles with sin, cos and tan (SOHCAHTOA), drawn to scale with steps. Free for geometry, GCSE and SAT.

Enter any two values (at least one side). The right angle is at C; c is the hypotenuse.

a = 3b = 4c = 5ABC36.87°53.13°
a
3
b
4
c
5
A
36.87°
B
53.13°
Area
6
Perimeter
12
  1. 1

    Pythagorean theorem for the hypotenuse

    c=a2+b2=32+42=5c = \sqrt{a^2 + b^2} = \sqrt{3^2 + 4^2} = 5
  2. 2

    TOA: tan A = opposite / adjacent

    A=tan⁡−1 ⁣(ab)=tan⁡−1 ⁣(34)=36.87∘A = \tan^{-1}\!\left(\frac{a}{b}\right) = \tan^{-1}\!\left(\frac{3}{4}\right) = 36.87^\circ
  3. 3

    The other acute angle

    B=90∘−A=53.13∘B = 90^\circ - A = 53.13^\circ
  4. 4

    Area and perimeter

    Area=12ab=6,Perimeter=a+b+c=12\text{Area} = \tfrac12 ab = 6,\quad \text{Perimeter} = a+b+c = 12

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FAQ

What is the Pythagorean theorem?

In a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle).

What does SOHCAHTOA stand for?

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

What do I need to solve a right triangle?

Two values, at least one of them a side. Two angles alone fix the shape but not the size.

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