• Pythagoras Theorem

    Pythagoras Theorem applies to right angled triangles.

    A right angle triangle - Figure to the right - is a triangle with one angle equals to 90°. The side opposite to this angle is known as the Hypotenuse.
    For angle A, side b is known as the adjacent and side a is known as the opposite.
    Equally, for angel B, side a is known as the adjacent and side b is known as the opposite.

    Pythagoras' theorem states that for all right angle triangles "The square constructed on the longest side - hypotenuse- of the triangle, is equal to the sum of the squares constructed on the other two sides of the triangle"
    Example: A triangle with sides 5,4 and 3. 52 = 42 + 32 as shown in the Fig 2.
    The inner radius, r, the radius of a circle inside the triangle, is given by the following formula from Fig 1: r = a * b / (a + b + H)
    The outer radius, R the radius of a circle surrounding the triangle is R = H / 2.

    Images and tables

    pythagoras2 pythagoras2

Pythagoras Triangles Tool

This program will find all the right angle triangles between either two values for the sides' lengths or between two complementary angles. Complementary angles are two angles which add up 90°.

From the dropdown below,
find all right angle triangles using:


To see a graphical representation of any triangle, click on the botton on the left most column of the selected triangle.

# Sides Angles Circles' radii
hypo side side angle angle r R

Graphical Representation of the selected triangle