Lösung 4.1:3b
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Version vom 14:44, 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{.} |
