Height and DistanceHard

Question

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation at apoint O on this line and all the poles are on the same side of O. If the height of the longest pole is ′h′ and thedistance of the foot of the smallest pole from O is ′a′; then the distance between two consecutive poles, is :

Options

A.
B.
C.
D.

Solution


ᐃOA1B1, ᐃOA2B2, ᐃOA3B3, ....., ᐃOA10B10 are similar.
⇒ = tan α.
∵ h10 = h = a10 tan α            ......... (1)
and a1 = a⇒ h1 = a tan α        ......... (2)
⇒  h = (a + 9d) tan a where d is distance between poles
⇒ h = a tanα + 9d tanα
⇒ = d
⇒ d =

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