From Förberedande kurs i matematik 1

Revision as of 09:34, 9 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 4.1:3b moved to Solution 4.1:3b: Robot: moved page) ← Previous diff		Current revision (08:06, 3 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	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.
-	<center> [[Image:4_1_3b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	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>}}
		+
		+	i.e.
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		+	{{Displayed math||<math>x^{2}=13^{2}-12^{2}\,\textrm{.}</math>}}
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		+	This means that
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		+	{{Displayed math||<math>x = \sqrt{13^{2}-12^{2}} = \sqrt{169-144} = \sqrt{25} = 5\,\textrm{.}</math>}}

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Current revision

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{.}