Solution 4.1:3c

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In this right-angled triangle, the side of length
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<center> [[Image:4_1_3c.gif]] </center>
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<math>\text{17}</math>
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is the hypotenuse (it is the side which is opposite the right angle). Pythagoras' theorem then gives
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<math>\text{17}^{2}=8^{2}+x^{2}</math>
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or
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<math>x^{2}=\text{17}^{2}-8^{2}</math>
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We get
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<math>\begin{align}
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& x=\sqrt{\text{17}^{2}-8^{2}}=\sqrt{289-64}=\sqrt{225} \\
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& =\sqrt{9\centerdot 25}=\sqrt{3^{2}\centerdot 5^{2}}=3\centerdot 5=15. \\
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\end{align}</math>

Revision as of 09:36, 27 September 2008

In this right-angled triangle, the side of length \displaystyle \text{17} is the hypotenuse (it is the side which is opposite the right angle). Pythagoras' theorem then gives


\displaystyle \text{17}^{2}=8^{2}+x^{2}


or


\displaystyle x^{2}=\text{17}^{2}-8^{2}


We get


\displaystyle \begin{align} & x=\sqrt{\text{17}^{2}-8^{2}}=\sqrt{289-64}=\sqrt{225} \\ & =\sqrt{9\centerdot 25}=\sqrt{3^{2}\centerdot 5^{2}}=3\centerdot 5=15. \\ \end{align}

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