Question 18

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waecmaths question: 

In diagram \[\left| QR \right|=10m,\text{ }\left| SR \right|=8m,\]\[\angle QPS={{30}^{\circ }},\angle QRP={{90}^{\circ }}\text{ and }\left| PS \right|=x\]find x

Option A: 

1.32m

Option B: 

6.32m

Option C: 

9.32m

Option D: 

17.32m

waecmaths solution: 

$\begin{align}  & \tan \theta =\frac{opposite}{adjacent}=\frac{\left| QR \right|}{\left| PR \right|} \\ & \tan {{30}^{\circ }}=\frac{10}{8+x} \\ & \frac{1}{\sqrt{3}}=\frac{10}{8+x} \\ & 8+x=10\sqrt{3} \\ & 8+x=17.32 \\ & x=9.32 \\\end{align}$

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