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Right-angled Triangles, SM-Bank 020

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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\(\text{Let }a=1.5 ,\ b=2\ \text{and }c=2.5\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=1.5^2+2^2\)
    \(=2.25+4\)
    \(=6.25\)
    \(=2.5^2\)
    \(=\text{RHS}\)

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