From Förberedande kurs i matematik 1

Revision as of 12:55, 2 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:4_1_3b.gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (08:06, 3 October 2008) (edit) (undo) Tek (Talk | contribs) m
(3 intermediate revisions not shown.)
Line 1:		Line 1:
-	{{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> [[Bild: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
		+
		+	{{Displayed math||<math>13^{2} = 12^{2} + x^{2}\,,</math>}}
		+
		+	i.e.
		+
		+	{{Displayed math||<math>x^{2}=13^{2}-12^{2}\,\textrm{.}</math>}}
		+
		+	This means that
		+
		+	{{Displayed math||<math>x = \sqrt{13^{2}-12^{2}} = \sqrt{169-144} = \sqrt{25} = 5\,\textrm{.}</math>}}

---

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{.}