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Solving Problem Involving Trigonometry

Solving Problem Involving Trigonometry

Secondary 3

Points \(P\), \(Q\), \(R\), \(S\) lie on a horizontal ground.
\(PQ=250\) m, \(SR=285\) m, \(\angle QPR=36{}^\circ\), \(\angle PSR=47{}^\circ\) and \(\angle SPR=70{}^\circ\).
Calculate

  1. the length of \(PR\),
  2. the length of \(QR\),
  3. the area of triangle \(PSR\),
  4. the shortest distance from \(Q\) to \(PR\).

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Answer:(i) \(222\text{ m}\) (ii) \(148\text{ m}\) (iii) \(28\,200\text{ m}^2\) (iv) \(147\text{ m}\)

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