Solution 4.1:3b

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Because one of the angles in the triangle is
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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.
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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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The side of length 13 is the hypotenuse in the triangle, and the Pythagorean theorem therefore gives us that
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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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{{Displayed math||<math>13^{2} = 12^{2} + x^{2}\,,</math>}}
i.e.
i.e.
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{{Displayed math||<math>x^{2}=13^{2}-12^{2}\,\textrm{.}</math>}}
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<math>x^{2}=13^{2}-12^{2}</math>
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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>}}
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<math>x=\sqrt{13^{2}-12^{2}}=\sqrt{169-144}=\sqrt{25}=5</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{.}
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