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3D Trigonometry: Geometric Analysis of a Right-Angled Triangular Prism

3D Trigonometry: Geometric Analysis of a Right-Angled Triangular Prism

Secondary 3

In the diagram below (not drawn to scale), \(E\), \(G\) and \(C\) represent three points.

Given that \(EG=1125\) m and \(CE=957\) m, the bearing of \(G\) from \(E\) is \(135{}^\circ\) and \(\angle CEG=60{}^\circ\).

Find

  1. the bearing of \(E\) from \(C\).
  2. the distance between \(C\) and \(G\).
  3. \(\angle EGC\).
  4. the bearing of \(C\) from \(G\).

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Answer:(i) \(015^\circ\) (ii) \(1050\text{ m}\) (iii) \(52.0^\circ\) (iv) \(263^\circ\)

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