Question

n the given figure if $AB=m(\sqrt{3}-1)$. Find m

Answer 1

Name the Inner triangle as BDC, where $\angle D={90}^{\circ }$
Now In $△BDC$,
$\tan 45=\frac{DC}{BD}$
$DC=BD=80$
In $△ADC$,
$\tan 30=\frac{DC}{AD}$
$AD=DC\sqrt{3}$
$AD=80\sqrt{3}$
$AB+BD=80\sqrt{3}$
$AB=80(\sqrt{3}-1)$
$AB=58.56$ m