Question 23

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waecmaths question: 

Given that  $\tan x=\tfrac{2}{3}$, where ${{0}^{\circ }}\le x\le {{90}^{\circ }}$, find the value of $2\sin x$

Option A: 

$\frac{2\sqrt{13}}{13}$

Option B: 

$\frac{3\sqrt{13}}{13}$

Option C: 

$\frac{4\sqrt{13}}{13}$

Option D: 

 $\frac{6\sqrt{13}}{13}$

waecmaths solution: 

$\begin{align}  & \left| BC \right|=\sqrt{{{2}^{2}}+{{3}^{2}}} \\ & BC=\sqrt{13} \\ & \sin x=\frac{opp}{hyp}=\frac{2}{\sqrt{13}} \\ & 2\sin x=2\times \frac{2}{\sqrt{13}}=\frac{4}{\sqrt{13}}=\frac{4}{\sqrt{13}}\times \frac{\sqrt{13}}{\sqrt{13}}=\frac{4\sqrt{13}}{13} \\\end{align}$

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