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

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) (h sin α + a text cos α /9 cos α ) (B) (h cos α - a s i n α /9 sin α ) (C) (h sin α + a text cos α /9 sin α ) (D) (h cos α - a text sin α /9 cos α )

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-fas5w0l04zso.png" /> from diagram tan α =(h/a + 9 b) a+9b=(h cos α /sin â¡ α ) 9b= (h cos α - a sin â¡ α /sin â¡ α ) b=(h cos α - a sin â¡ α /9 sin â¡ α )

$\frac{h s in α + a cos α}{9 cos α}$

$\frac{h cos α - a s in α}{9 s in α}$

$\frac{h s in α + a cos α}{9 s in α}$

$\frac{h cos α - a sin α}{9 cos α}$

from diagram
$t an α = \frac{h}{a + 9 b}$
$a + 9 b = \frac{h cos α}{s in α}$
$9 b = \frac{h cos α - a s in α}{s in α}$
$b = \frac{h cos α - a s in α}{9 s in α}$

9cosαhsinα+a cosα​

9sinαhcosα−asinα​

9sinαhsinα+a cosα​

9cosαhcosα−a sinα​

from diagram tanα=a+9bh​ a+9b=sin⁡αhcosα​ 9b=sin⁡αhcosα−asin⁡α​ b=9sin⁡αhcosα−asin⁡α​

$\frac{h s in α + a cos α}{9 cos α}$

$\frac{h cos α - a s in α}{9 s in α}$

$\frac{h s in α + a cos α}{9 s in α}$

$\frac{h cos α - a sin α}{9 cos α}$

from diagram
$t an α = \frac{h}{a + 9 b}$
$a + 9 b = \frac{h cos α}{s in α}$
$9 b = \frac{h cos α - a s in α}{s in α}$
$b = \frac{h cos α - a s in α}{9 s in α}$