Aus Online Mathematik Brückenkurs 1

Version vom 08:07, 3. Okt. 2008 (bearbeiten) Tek (Diskussion | Beiträge) ← Zum vorherigen Versionsunterschied		Version vom 08:47, 22. Okt. 2008 (bearbeiten) (rückgängig) Tekbot (Diskussion | Beiträge) K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)) Zum nächsten Versionsunterschied →
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	With the help of the Pythagorean theorem, we can write a relation between the sides of a right-angled triangle		With the help of the Pythagorean theorem, we can write a relation between the sides of a right-angled triangle
-	{{Displayed math||<math>x^2 = 30^2 + 40^2\,\textrm{.}</math>}}	+	{{Abgesetzte Formel||<math>x^2 = 30^2 + 40^2\,\textrm{.}</math>}}
	This equation gives us that		This equation gives us that
-	{{Displayed math||<math>\begin{align}	+	{{Abgesetzte Formel||<math>\begin{align}
	x &= \sqrt{30^{2}+40^{2}} = \sqrt{900+1600} = \sqrt{2500}\\[5pt]		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{.}		&= \sqrt{25\cdot 100} = \sqrt{5^{2}\cdot 10^{2}} = 5\cdot 10 = 50\,\textrm{.}
	\end{align}</math>}}		\end{align}</math>}}

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Version vom 08:47, 22. Okt. 2008

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}