The diagram above shows two rods $AB$ and $BC$ of length $4$ m and $9$ m respectively and \(

Question

The diagram above shows two rods $AB$ and $BC$ of length $4$ m and $9$ m respectively and $\angle ABC = 90^{\circ} $. Rollers are fixed at points $A$ and $B$ such that $A$ is able to move along the wall and $B$ is able to move along the celling. The horizontal distance of $C$ from the vertical wall is $d$ m. Show clearly that $d = 4\sin \theta + 9\cos \theta$.[2] Express $d$ in the form $R\cos(\theta - \alpha)$ where $R > 0$ and $0^{\circ} < \alpha < 90^{\circ}$.[4] Find the value of $\theta$ for which $d = 6\text{ m}$.[2] Find the maximum value of $d$ and the corresponding value of $\theta$.[2]

Accepted Answer

(b) $ \sqrt{97}\cos{ (\theta - 24.0^{\circ}) }$ (c) $76.4^{\circ}$ ($1$ d.p.) (d) Maximum value of $d = \sqrt{97}$, when $\theta = 24.0^{\circ}$

2024 FMSS PRELIMS P2 Q9

2024 FMSS PRELIMS P2 Q9