Choosing a cable for a spatial span

Choosing a cable for a spatial span

Secondary 3
6 marks
TGM Original Questions

A vertical post \(AT\) of height \(8\) m stands at corner \(A\) of a horizontal rectangular courtyard \(ABCD\), where \(AB=12\) m and \(BC=9\) m. A straight cable runs from \(T\) to the opposite corner \(C\). A total of \(1.2\) m of extra cable is needed for fittings. Cables are sold in lengths of \(18\) m or \(20\) m.

  1. Calculate the straight span \(CT\).[2]
  2. Choose the shortest cable that can be used, allowing for the fittings. Justify your choice.[2]
  3. The cable must make an angle of no more than \(30^\circ\) with the ground. Determine whether this condition is met.[2]

Solution:

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Answer:(a) \(17\text{ m}\) (b) \(20\text{ m}\) cable; \(18.2\text{ m}\) is required. (c) Yes; angle \(28.1^\circ\) (1 d.p.).

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