An internal point and an exact sine value

An internal point and an exact sine value

Secondary 2
TGM Original Questions

Triangle \(ABC\) is right-angled at \(A\), and \(M\) lies on \(AB\). Given \(AM=12\) cm, \(AC=BM\), and \(\tan\angle ABC=3/5\), find

  1. \(AC\),
  2. the area of \(\triangle BMC\),
  3. the exact value of \(\sin\angle AMC\).

Solution:

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Answer:(a) \(18\) cm; (b) \(162\text{ cm}^2\); (c) \(3\sqrt{13}/13\).

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