Aus Online Mathematik Brückenkurs 1

A right-angled triangle is a triangle in which one of the angles is 90°. The side which is opposite the 90°-angle is called the hypotenuse (marked x in the triangle) and the others are called opposite and the adjacent.

With the help of the Pythagorean theorem, we can write a relation between the sides of a right-angled triangle

\displaystyle x^2 = 30^2 + 40^2\,\textrm{.}

This equation gives us that

\displaystyle \begin{align} x &= \sqrt{30^{2}+40^{2}} = \sqrt{900+1600} = \sqrt{2500}\\[5pt] &= \sqrt{25\cdot 100} = \sqrt{5^{2}\cdot 10^{2}} = 5\cdot 10 = 50\,\textrm{.} \end{align}