Question 13

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waecmaths question: 

In the diagram $\left| QR \right|=5cm$ $\angle PQR={{60}^{\circ }}$ and $\angle PSR={{45}^{\circ }}$. Find $\left| PS \right|$ leaving your answer in surd form

Option A: 

$4\sqrt{5}cm$

Option B: 

$3\sqrt{7}cm$

Option C: 

$4\sqrt{6}cm$

Option D: 

$5\sqrt{6}cm$ 

waecmaths solution: 

$\begin{align}  & \left| PR \right|=5cm\tan {{60}^{\circ }}=5\sqrt{3}cm \\ & \sin {{45}^{\circ }}=\frac{5\sqrt{3}}{\left| PS \right|} \\ & PS=\frac{5\sqrt{3}}{\sin {{45}^{\circ }}}=\frac{5\sqrt{3}}{{1}/{\sqrt{2}}\;}=5\sqrt{3}\times \sqrt{2}=5\sqrt{6} \\\end{align}$

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