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Lösung 4.1:3b

Aus Online Mathematik Brückenkurs 1

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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
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{{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
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{{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>}}

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

132=122+x2

i.e.

x2=132−122.

This means that

x=132−122=169−144=25=5. 
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.1:3b“