Question

$n$ poles standing at equal distances on a straight road subtend the same angle $\alpha$ at a point $O$ on the road. If the height of the largest pole is $h$ and the distance of the foot of the smallest pole from $O$ is $a$, the distance between two consecutive poles is:

• A. $\frac{h\sin \alpha -a\cos \alpha }{(n-1)\sin \alpha }$
• B. $\frac{h\cos \alpha -a\cos \alpha }{(n-1)\cos \alpha }$
• C. $\frac{h\cos \alpha -a\sin \alpha }{(n-1)\sin \alpha }$
• D. $\frac{h\sin \alpha -a\cos \alpha }{(n-1)\cos \alpha }$

Answer 1

The correct option is C $\frac{h\cos \alpha -a\sin \alpha }{(n-1)\sin \alpha }$

$\frac{h}{a+(n-1)x}=\frac{y}{a}\cdot y=a\tan \alpha$

or, $\frac{h}{a+(n-1)x}=\frac{y}{a}\cdot y=\frac{a\tan \alpha }{a}$

or, $\frac{h}{a+(n-1)x}=\frac{y}{a}\cdot y=\tan \alpha$

or, $\frac{h}{\tan \alpha }=a+(n-1)x$

or, $(n-1)x=h-a\tan \alpha$

or, $x=\frac{h-a\tan \alpha }{(n-1)\times \tan \alpha }$

or,$x=\frac{h\cos \alpha -a\sin \alpha }{(n-1)\cos \alpha \times \tan \alpha }$

or, $x=\frac{h\cos \alpha -a\sin \alpha }{(n-1)\sin \alpha }$