A Pythagorean triangle attached to a 45-degree triangle

A Pythagorean triangle attached to a 45-degree triangle

Secondary 2
6 marks
TGM Original Questions

Core stretch

In the diagram, \(AC=5\) cm, \(BC=12\) cm, \(\angle ACB=90^\circ\), and \(\angle ADC=45^\circ\). Find

    1. \(AB\),[2]
    2. \(DB\)[2]
  1. determine whether \(\angle BAD=90^\circ\), showing your working.[2]

Give non-exact lengths and areas to 3 significant figures, and angles to 1 decimal place.

Solution:

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Answer:(a)(i) \(13\) cm (ii) \(17\) cm (b) No, \(\angle BAD\ne90^\circ\).

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