Compound triangle from a given area

Compound triangle from a given area

Secondary 2
6 marks
TGM Original Questions

Points \(A,B,P\) lie on a straight line, with \(B\) between \(A\) and \(P\), and \(BC\perp AP\). Given \(AP=18\) cm, \(AC=15\) cm and the area of \(\triangle APC\) is \(81\text{ cm}^2\), find

  1. \(BC\),[2]
  2. \(CP\),[2]
  3. \(\angle CPA\). [2]

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

Solution:

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Answer:(a) \(9\) cm (b) \(3\sqrt{13}\approx10.8\) cm (c) \(56.3^\circ\).

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