Solution 4.1:3a
From Förberedande kurs i matematik 1
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- | {{ | + | A right-angled triangle is a triangle in which one of the angles is 90°. The side which is opposite the 90°-angle is called the hypotenuse (marked ''x'' in the triangle) and the others are called opposite and the adjacent. |
- | < | + | |
- | {{ | + | With the help of the Pythagorean theorem, we can write a relation between the sides of a right-angled triangle |
+ | |||
+ | {{Displayed math||<math>x^2 = 30^2 + 40^2\,\textrm{.}</math>}} | ||
+ | |||
+ | This equation gives us that | ||
+ | |||
+ | {{Displayed math||<math>\begin{align} | ||
+ | x &= \sqrt{30^{2}+40^{2}} = \sqrt{900+1600} = \sqrt{2500}\\[5pt] | ||
+ | &= \sqrt{25\cdot 100} = \sqrt{5^{2}\cdot 10^{2}} = 5\cdot 10 = 50\,\textrm{.} | ||
+ | \end{align}</math>}} |
Current revision
A right-angled triangle is a triangle in which one of the angles is 90°. The side which is opposite the 90°-angle is called the hypotenuse (marked x in the triangle) and the others are called opposite and the adjacent.
With the help of the Pythagorean theorem, we can write a relation between the sides of a right-angled triangle
\displaystyle x^2 = 30^2 + 40^2\,\textrm{.} |
This equation gives us that
\displaystyle \begin{align}
x &= \sqrt{30^{2}+40^{2}} = \sqrt{900+1600} = \sqrt{2500}\\[5pt] &= \sqrt{25\cdot 100} = \sqrt{5^{2}\cdot 10^{2}} = 5\cdot 10 = 50\,\textrm{.} \end{align} |