The diagram shows two rods $AB$ and $BC$ of length $2$ m and $5$ m respectively, joined toge

Question

The diagram shows two rods $AB$ and $BC$ of length $2$ m and $5$ m respectively, joined together at $B$ such that $\angle ABC=90{}^\circ $. Small rings are attached to $A$ and $C$ so that $A$ can move along the vertical pole $OY$ and $C$ can move along the horizontal pole $OX$. The rod $BC$ makes an angle $\theta$ with $OX$. Show that $OA = 5\sin \theta - 2\cos \theta$ Express $OA$ in the form $R\sin (\theta-\alpha) $ where $R > 0$ and $0^\circ < \alpha < 90^\circ$ Given that $A$ can be no higher than $3.5$ m above $O$ , calculate the greatest possible valuer of $\theta$

Accepted Answer

(i) $OA=5\sin\theta-2\cos\theta$ (ii) $OA=\sqrt{29}\sin(\theta-21.8^\circ)$ (iii) $\theta_{\max}=62.3^\circ$

2025 CHS PRELIMS P2 Q8

2025 CHS PRELIMS P2 Q8

Solution:

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