Two poles are 10m and 20 m high. The line joining their tops makes an angle of 15º with the horizontal. What is the approximate distance between the poles?
Solution
$\tan 15^{\circ} = \dfrac{AB}{BE}$
$\tan (45^{\circ} - 30^{\circ}) = \dfrac{10}{BE} (AB = 20 - 10)$
$\Rightarrow \dfrac{\tan 45^{\circ} - \tan 30^{\circ}}{1 + \tan 45^{\circ} \tan 30^{\circ}} = \dfrac{10}{BE}~~~~$(Using $\tan$(A - B))
$\Rightarrow \dfrac{\sqrt{3} - 1}{\sqrt{3} + 1} = \dfrac{10}{BE}$
BE = 37.3m
Distance between poles = 37.3m