Question
Find the length of $EC.$
✓
Answer
$CD =28 \ cm$
$ \Rightarrow AB =28 \ cm$
In right $\triangle ABE ,$
$ \tan 30^{\circ}=\frac{ BE }{ AB }$
$ \Rightarrow \frac{1}{\sqrt{3}}=\frac{ BE }{28}$
$ \Rightarrow BE =\frac{28}{\sqrt{3}}$
In right $\triangle ABC$,
$\tan 60^{\circ}=\frac{ CB }{ AB }$
$ \Rightarrow \sqrt{3}=\frac{ CB }{28}$
$ \Rightarrow CB =28 \sqrt{3}$
$\therefore$ Length of $EC$
$ = CB + BE$
$ =28 \sqrt{3}+\frac{28}{\sqrt{3}}$
$ =\frac{84+28}{\sqrt{3}}$
$ =\frac{112}{\sqrt{3}} .$
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