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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 hcosα−asinα9sinαSince all 10 poles are subtending equal angles at O. Let the distance between two consecutive poles =d.Distance form O to the smallest pole =aTotal base distance in right angled triangle =a+9dtanα=ha+9d9dtanα+atanα=hd=h−atanα9tanα=h−asinαcosα9sinαcosα=hcosα−asinα9sinα

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