Two right triangles and a midpoint area

Two right triangles and a midpoint area

Secondary 2
TGM Original Questions

Points \(B,C,D\) are collinear. Given \(AC=10\) cm, \(AD=10\sqrt2\) cm, \(\angle ACB=\angle ACD=90^\circ\), and \(\angle ABC=30^\circ\), calculate

  1. \(AB\),
  2. \(\angle DAC\),
  3. the area of \(\triangle CAX\), where \(X\) is the midpoint of \(AD\) and \(CX\perp AD\).

Solution:

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Answer:(a) \(20\) cm; (b) \(45^\circ\); (c) \(25\text{ cm}^2\).

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