Solution 4.1:3b

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m (Lösning 4.1:3b moved to Solution 4.1:3b: Robot: moved page)
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Because one of the angles in the triangle is
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<center> [[Image:4_1_3b.gif]] </center>
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<math>90^{\circ }</math>, we have a right-angled triangle and can use Pythagoras' theorem to set up a relation between the triangle's sides.
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The side of length
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<math>\text{13}</math>
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is the hypotenuse in the triangle, and Pythagoras' theorem therefore gives us that
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<math>13^{2}=12^{2}+x^{2}</math>
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i.e.
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<math>x^{2}=13^{2}-12^{2}</math>
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This means that
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<math>x=\sqrt{13^{2}-12^{2}}=\sqrt{169-144}=\sqrt{25}=5</math>

Revision as of 09:32, 27 September 2008

Because one of the angles in the triangle is \displaystyle 90^{\circ }, we have a right-angled triangle and can use Pythagoras' theorem to set up a relation between the triangle's sides.

The side of length \displaystyle \text{13} is the hypotenuse in the triangle, and Pythagoras' theorem therefore gives us that


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


i.e.


\displaystyle x^{2}=13^{2}-12^{2}


This means that


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

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