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Nov 2002 p1 q6
565

In the diagram, triangle ABC is right-angled and D is the mid-point of BC. Angle DAC is \(30^\circ\) and angle BAD is \(x^\circ\). Denoting the length of AD by l,

  1. express each of AC and BC exactly in terms of l, and show that \(AB = \tfrac{1}{2}l\sqrt{7}\),
  2. show that \(x = \tan^{-1}\!\left(\frac{2}{\sqrt{3}}\right) - 30^\circ\).
problem image 565
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