Question 31

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waecmaths question: 

In the diagram$\left| PQ \right|=4cm$, $\left| QR \right|=6cm,\text{ }\left| RS \right|=12cm$ $\angle QRS={{90}^{\circ }}$. Find the value of x

Option A: 

27

Option B: 

26

Option C: 

18

Option D: 

13

waecmaths solution: 

$\begin{align}  & \vartriangle QSR \\ & \tan \theta =\frac{\left| SQ \right|}{\left| SR \right|}=\frac{6}{12}=\frac{1}{2} \\ & \theta ={{\tan }^{-1}}(\tfrac{1}{2})\simeq {{27}^{\circ }} \\ & \vartriangle PSR \\ & \tan \beta =\frac{\left| PR \right|}{\left| SR \right|}=\frac{10}{12}=\frac{5}{6} \\ & \beta ={{\tan }^{-1}}(\tfrac{5}{6})\simeq 40 \\ & x=\beta -\theta ={{40}^{\circ }}-{{27}^{\circ }}={{13}^{\circ }} \\\end{align}$

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