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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

A
hsinα+acosα9cosα
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B
hcosαasinα9sinα
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C
hsinα+acosα9sinα
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D
hcosαasinα9cosα
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Solution

The correct option is B hcosαasinα9sinα
Since all 10 poles are subtending equal angles at O. Let the distance between two consecutive poles =d.
Distance form O to the smallest pole =a
Total base distance in right angled triangle =a+9d
tanα=ha+9d
9dtanα+atanα=h
d=hatanα9tanα
=hasinαcosα9sinαcosα
=hcosαasinα9sinα

283040_310009_ans_cea467ebc58f41579cdce091aa12fdd9.png

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