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Right-angled Triangles, SM-Bank 031

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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\(a=\sqrt{115}\)

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

\(\text{Let }b=9\ \text{and }c=14\)

\(a^2+9^2\) \(=14^2\)
\(a^2+81\) \(=196\)
\(a^2\) \(=196-81\)
\(a^2\) \(=115\)
\(\therefore a\) \(=\sqrt{115}\)