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Right-angled Triangles, SM-Bank 030

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

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\(a=28.3\ \text{(1 d.p.)}\)

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

\(\text{Let }b=98\ \text{and }c=102\)

\(a^2+98^2\) \(=102^2\)
\(a^2+9604\) \(=10404\)
\(a^2\) \(=10404-9604\)
\(a^2\) \(=800\)
\(\therefore a\) \(=\sqrt{800}\)
  \(=28.284\dots\approx 28.3\ \text{(1 d.p.)}\)