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A man sees the top of a flag post at the angle of elevation 60 degree from a point "a" meter away from the base of the post. He sees the top at the angle

of elevation at 30 degree from the distance "b" from the base. Show that the height of the post ie "h"=√ab ???


Tan60 =  \frac{h}{a}   \Rightarrow   \sqrt{3} =  \frac{h}{a}    ....(1)

Tan30 =  \frac{h}{b}   \Rightarrow    \frac{1}{\sqrt{3}}  =  \frac{h}{b} \Rightarrow \sqrt{3} = \frac{b}{h} .(2)

From (1) and (2)

\frac{h}{a} = \frac{b}{h}

⇒ h² = ab

⇒ h =  \sqrt{ab}

2 5 2
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