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Right-angled Triangles, SM-Bank 033

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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\(a=\sqrt{45}\)

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

\(\text{Let }b=6\ \text{and }c=9\)

\(a^2+6^2\) \(=9^2\)
\(a^2+36\) \(=81\)
\(a^2\) \(=81-36\)
\(a^2\) \(=45\)
\(\therefore a\) \(=\sqrt{45}\)