Aus Online Mathematik Brückenkurs 1

Version vom 08:06, 3. Okt. 2008 (bearbeiten) Tek (Diskussion | Beiträge) K ← 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 →
Zeile 3:		Zeile 3:
	The side of length 13 is the hypotenuse in the triangle, and the Pythagorean theorem therefore gives us that		The side of length 13 is the hypotenuse in the triangle, and the Pythagorean theorem therefore gives us that
-	{{Displayed math||<math>13^{2} = 12^{2} + x^{2}\,,</math>}}	+	{{Abgesetzte Formel||<math>13^{2} = 12^{2} + x^{2}\,,</math>}}
	i.e.		i.e.
-	{{Displayed math||<math>x^{2}=13^{2}-12^{2}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel||<math>x^{2}=13^{2}-12^{2}\,\textrm{.}</math>}}
	This means that		This means that
-	{{Displayed math||<math>x = \sqrt{13^{2}-12^{2}} = \sqrt{169-144} = \sqrt{25} = 5\,\textrm{.}</math>}}	+	{{Abgesetzte Formel||<math>x = \sqrt{13^{2}-12^{2}} = \sqrt{169-144} = \sqrt{25} = 5\,\textrm{.}</math>}}

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Version vom 08:47, 22. Okt. 2008

Because one of the angles in the triangle is 90°, we have a right-angled triangle and can use the Pythagorean theorem to set up a relation between the triangle's sides.

The side of length 13 is the hypotenuse in the triangle, and the Pythagorean theorem therefore gives us that

\displaystyle 13^{2} = 12^{2} + x^{2}\,,

i.e.

\displaystyle x^{2}=13^{2}-12^{2}\,\textrm{.}

This means that

\displaystyle x = \sqrt{13^{2}-12^{2}} = \sqrt{169-144} = \sqrt{25} = 5\,\textrm{.}