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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<center> [[Image:4_1_3a.gif]] </center>
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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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angled triangle:
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<math>x^{2}=30^{2}+40^{2}</math>
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This equation gives us that
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<math>\begin{align}
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& x=\sqrt{30^{2}+40^{2}}=\sqrt{900+1600}=\sqrt{2500} \\
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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>

Revision as of 09:26, 27 September 2008

A right-angled triangle is a triangle in which one of the angles is \displaystyle 90^{\circ }. The side which is opposite the \displaystyle 90^{\circ } -angle is called the hypotenuse (marked \displaystyle 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}


This equation gives us that


\displaystyle \begin{align} & x=\sqrt{30^{2}+40^{2}}=\sqrt{900+1600}=\sqrt{2500} \\ & =\sqrt{25\centerdot 100}=\sqrt{5^{2}\centerdot 10^{2}}=5\centerdot 10=50 \\ \end{align}

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