On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 40 m long and the shadow is 32 m, how tall is the flag pole?

Using Pythagoras's theorem we can write,  (Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2  Here the hypotenuse and base (shadow) are given and we have to find the length of the flag pole i.e. The perpendicular to the shadow.  So  (Perpendicular)^2 = (40)^2 - (32)^2  Using a62 - b^2 = (a+b)(a-b) we can write  (Perpendicular)^2 = (40+32)(40-32) = 72 * 8 = 9 * 8 * 8  => Perpendicular = Height of flag pole = sqrt (9 * 8 * 8) = 3 * 8 = 24 meters