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Right-angled Triangles, SM-Bank 032

Find the value of the pronumeral in the right-angled triangle below giving your answer in exact surd form.  (2 marks)

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\(a=\sqrt{176}\)

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\(\text{Pythagoras’ Theorem states:  }a^2+b^2=c^2\)

\(\text{Let }b=20\ \text{and }c=24\)

\(a^2+20^2\) \(=24^2\)
\(a^2+400\) \(=576\)
\(a^2\) \(=576-400\)
\(a^2\) \(=176\)
\(\therefore a\) \(=\sqrt{176}\)