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3D Problems Q1

3D Problems Q1

The diagram shows a pyramid with horizontal rectangular base \(ABCD\), where \(AB=8\) cm, \(BC=6\) cm. The vertex \(V\) of the pyramid is vertically above the centre of the base and the length of \(VA\) is \(9\) cm. The points \(E\), \(F\) are the mid-points of \(VA\), \(VD\) respectively. The point \(N\) is on \(VB\) such that \(VN:NB=2:1\).

Giving each answer correct to \(3\) significant, figures, find

  1. the angle between plane \(EFCB\) and the base,
  2. the angle which \(CN\) makes with the base.

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Answer:θ = 31.9° (1 d.p.); Angle between CN and base = 25.7° (1 d.p.)

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