Question

Let $10$ vertical poles standing at equal distances on a straight line, subtend the same angle of elevation $\alpha $ 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. $\frac{h sin \alpha + a \text{ cos} \alpha }{9 \, cos \alpha }$
• B. $\frac{h cos \alpha - a \, s i n \alpha }{9 sin \alpha }$
• C. $\frac{h sin \alpha + a \text{ cos} \alpha }{9 sin \alpha }$
• D. $\frac{h cos \alpha - a \text{ sin} \alpha }{9 cos \alpha }$

Answer 1

Answer: (B)

from diagram
$tan \alpha =\frac{h}{a + 9 b}$
$a+9b=\frac{h cos \alpha }{sin ⁡ \alpha }$
$9b= \, \frac{h cos \alpha - a sin ⁡ \alpha }{sin ⁡ \alpha }$
$b=\frac{h cos \alpha - a sin ⁡ \alpha }{9 sin ⁡ \alpha }$