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Right-angled Triangles, SM-Bank 029

Find the value of the pronumeral in the right-angled triangle below correct to one decimal place.  (2 marks)

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\(a=15.7\ \text{(1 d.p.)}\)

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

\(\text{Let }b=14\ \text{and }c=21\)

\(a^2+14^2\) \(=21^2\)
\(a^2+196\) \(=441\)
\(a^2\) \(=441-196\)
\(a^2\) \(=245\)
\(\therefore a\) \(=\sqrt{245}\)
  \(=15.652\dots\approx 15.7\ \text{(1 d.p.)}\)