Solution 4.1:3b
From Förberedande kurs i matematik 1
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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. |
- | < | + | |
- | {{ | + | 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>}} | ||
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+ | 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>}} |
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{.} |