Question

Two men standing on same side of a pillar 75 metre high, observe the angles of elevation of the top of the pillar to be 30° and 60° respectively the distance between two men is​

Answer 1

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Answer 2

Given :

Height of pillar = 75 m

Angle of elevation = 30° and 60° respectively

To find :

Distance between two men = ?

Solution :

Using the relation between height and distance :

$height=\dfrac{Distance}{\cot 30-\cot 60}\\\\75=\dfrac{distance}{\sqrt{3}-\dfrac{1}{\sqrt{3}}}\\\\75=\dfrac{distance\times \sqrt{3}}{3-1}\\\\75\times 2=\sqrt{3}\times distance\\\\150=\sqrt{3}\times distance\\\\\dfrac{150}{\sqrt{3}}=distance\\\\50\sqrt{3}=Distance$

Hence, the distance between two men is $50\sqrt{3}\ m$.