Solution 4.1:3a

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A right-angled triangle is a triangle in which one of the angles is
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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.
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<math>90^{\circ }</math>. The side which is opposite the
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<math>90^{\circ }</math>
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-angle is called the hypotenuse (marked
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<math>x</math>
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in the triangle) and the others are called opposite and the adjacent.
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With the help of Pythagoras' theorem, we can write a relation between the sides of a right
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With the help of Pythagoras' theorem, we can write a relation between the sides of a right-angled triangle
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angled triangle:
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<math>x^{2}=30^{2}+40^{2}</math>
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{{Displayed math||<math>x^2 = 30^2 + 40^2\,\textrm{.}</math>}}
This equation gives us that
This equation gives us that
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{{Displayed math||<math>\begin{align}
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<math>\begin{align}
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x &= \sqrt{30^{2}+40^{2}} = \sqrt{900+1600} = \sqrt{2500}\\[5pt]
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& x=\sqrt{30^{2}+40^{2}}=\sqrt{900+1600}=\sqrt{2500} \\
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&= \sqrt{25\cdot 100} = \sqrt{5^{2}\cdot 10^{2}} = 5\cdot 10 = 50\,\textrm{.}
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& =\sqrt{25\centerdot 100}=\sqrt{5^{2}\centerdot 10^{2}}=5\centerdot 10=50 \\
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\end{align}</math>}}
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\end{align}</math>
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Revision as of 08:04, 3 October 2008

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 Pythagoras' 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}

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