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Three-Dimensional Trigonometry: Analysis of a Right Square-Base Pyramid

Three-Dimensional Trigonometry: Analysis of a Right Square-Base Pyramid

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The diagram below shows a right square-base pyramid \(PQRS\) with \(PQ=13\) cm.
The midpoint of \(RS\) is \(M\).
The height \(VO\) of the pyramid is \(10\) cm.
Calculate

  1. the length of the diagonal \(QS\),
  2. the length \(OM\),
  3. the angle \(VSQ\),
  4. the volume of the pyramid.

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Answer:(i) \(QS=18.4\text{ cm}\) (ii) \(OM=6.5\text{ cm}\) (iii) \(\angle VSQ=47.4^\circ\) (iv) \(563\dfrac13\text{ cm}^3\)

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