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Question:

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point 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 the distance of the foot of the smallest pole from O is a; then the distance between two consecutive poles is?

hcosα−asinα9sinα

hsinα+acosα9sinα

hsinα+acosα9cosα

hcosα−asinα9cosα

Solution:

Since all 10 poles are subtending equal angles at O. Let the distance between two consecutive poles = d. Distance from O to the smallest pole = a
Total base distance in right angled triangle = a + 9d
tanα = h/(a + 9d)
9d tanα + a tanα = h
d = (h - a tanα)/(9 tanα) = (h - asinα/cosα)/(9sinα/cosα) = (hcosα - asinα)/(9sinα)