waecmaths question:
In the diagram TX is perpendicular to UW, $\left| UX \right|=1cm$and $\left| TX \right|=\left| WX \right|=\sqrt{3}cm$ Find $\angle UTW$
Option A:
135o
Option B:
105o
Option C:
75o
Option D:
60o
waecmaths solution:
$\begin{align} & \vartriangle TUX \\ & \angle XTU=\beta \\ & \tan \beta =\frac{opp}{adj}=\frac{UX}{TX} \\ & \tan \beta =\frac{1}{\sqrt{3}} \\ & \beta ={{\tan }^{-1}}(\tfrac{1}{\sqrt{3}})={{30}^{\circ }} \\ & \vartriangle TXW \\ & \angle XTW=\alpha \\ & \tan \alpha =\frac{opp}{adj}=\frac{XW}{TX} \\ & \tan \alpha =\frac{\sqrt{3}}{\sqrt{3}}=1 \\ & \alpha ={{\tan }^{-1}}(1)={{45}^{\circ }} \\ & \angle UTW=\alpha +\beta ={{45}^{\circ }}+{{30}^{\circ }}={{75}^{\circ }} \\\end{align}$
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