Question

Two poles of equal height stand vertically opposite to each other on either side of the road, which is 100 m wide. From a point on the road between the poles, the angle of elevation of the tops of the poles are 30 degree and 60 degree . Find the heights of the poles. Also find the distance of the point from the feets to the poles.​

Answer 1

$\huge{\orange{\boxed{\fcolorbox{lime}{aqua}{\pink{SOLUTION}}}}}$

In ∆AOC,

$\bf{\tan{60°}\:=\:\dfrac{h}{x}\:}$

$\therefore\:\bf{x\:=\:\dfrac{h}{\sqrt{3}}\:}$

In ∆BOD,

$\bf{\tan{30°}\:=\:\dfrac{h}{100\:-\:x}\:}$

$\implies\:\bf{100\:-\:x\:=\:{h}{\sqrt{3}}\:}$

$\implies\:\bf{100\:-\:{h}{\sqrt{3}}\:=\:x\:}$

$\implies\:\bf{100\:-\:{h}{\sqrt{3}}\:=\:\dfrac{h}{\sqrt{3}}\:}$

$\implies\:\bf{h\:=\:25\sqrt{3}\:m\:}$

$\therefore\:\bf{x\:=\:\dfrac{h}{\sqrt{3}}\:=\:\dfrac{25\sqrt{3}}{\sqrt{3}}}$

$\therefore\:\bf{x\:=\:25\:m\:}$

• OC = 25 m

→ OD = 100 - 25

→ OD = 75 m

$\mathbb{\blue{Hope\: it's\: help\:U}$