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Right-angled Triangles, SM-Bank 021

Use Pythagoras' Theorem to decide if the triangle below is right-angled.  (2 marks)

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\(\text{See worked solution}\)

\(\text{The triangle is right-angled as the sides form a Pythagorean triad.}\)

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\(\text{Let }a=13 ,\ b=84\ \text{and }c=85\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=13^2+84^2\)
    \(=169+7056\)
    \(=7225\)
    \(=85^2\)
    \(=\text{RHS}\)

\(\therefore\ \text{The triangle is right-angled as the sides form a Pythagorean triad.}\)