Trigonometry

Trigonometry

Secondary 4

A lifting arm consists of two straight links \(PQ=5\text{ m}\) and \(QR=12\text{ m}\). Both links rise to the right.

- \(PQ\) makes an angle \(\theta\) with the vertical.
- \(QR\) makes the same angle \(\theta\) with the horizontal.
- \(0^\circ<\theta<90^\circ\).

The diagram is schematic.

Let \(H\) be the vertical height of \(R\) above \(P\).

  1. Show that \(H=5\cos\theta+12\sin\theta\).

  2. Express \(H\) as \(R\sin(\theta+\alpha)\).

  3. Find the maximum height and the corresponding \(\theta\).

  4. Find all permitted values of \(\theta\) when \(H=12\text{ m}\).

Similar questions are unavailable for this question.
Answer:\(H=13\sin(\theta+22.6^\circ)\); maximum \(13\text{ m}\) at \(67.4^\circ\); \(H=12\) at \(44.8^\circ\).

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