Let 10 vertical poles standing at equal dista | vedclass

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Question

(A) Let the poles be at positions $A_1, A_2, ..., A_{10}$ with heights $h_1, h_2, ..., h_{10}$.Since all poles subtend the same angle $\alpha$ at $O$,

Vedclass · Accepted Answer

$\frac{h \cos \alpha - a \sin \alpha}{9 \sin \alpha}$

Vedclass · Answer

(A) Let the poles be at positions $A_1, A_2, ..., A_{10}$ with heights $h_1, h_2, ..., h_{10}$.Since all poles subtend the same angle $\alpha$ at $O$,we have $\frac{h_n}{OA_n} = 	an \alpha$ for all $n = 1, 2, ..., 10$.Given $OA_1 = a$ and $h_{10} = h$.Let $d$ be the distance between consecutive poles. Then $OA_{10} = OA_1 + 9d = a + 9d$.From the relation $\frac{h_{10}}{OA_{10}} = 	an \alpha$,we have $\frac{h}{a + 9d} = 	an \alpha$.Rearranging for $d$:$a + 9d = \frac{h}{	an \alpha} = h \cot \alpha$$9d = h \cot \alpha - a$$9d = \frac{h \cos \alpha}{\sin \alpha} - a = \frac{h \cos \alpha - a \sin \alpha}{\sin \alpha}$$d = \frac{h \cos \alpha - a \sin \alpha}{9 \sin \alpha}$.

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