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 :
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 :
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The foot of the longest pole is at distance a + 9d from O, and its height is that distance times tan(alpha).
Updated On: Nov 11, 2026
- \(\frac{h\sin\alpha+a\cos\alpha}{9\sin\alpha}\)
- \(\frac{h\cos\alpha-a\sin\alpha}{9\cos\alpha}\)
- \(\frac{h\cos\alpha-a\sin\alpha}{9\sin\alpha}\)
- \(\frac{h\sin\alpha+a\cos\alpha}{9\cos\alpha}\)
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The Correct Option is C
Solution and Explanation
Step 1: Let the common gap be \(d\). The feet are at distances \(a,\ a+d,\dots,a+9d\) from O; the longest pole is the farthest one.
Step 2: All poles subtend angle \(\alpha\) at O, so the tops lie on a line through O: \(\tan\alpha=\frac{h}{a+9d}\).
Step 3: \(9d=h\cot\alpha-a=\frac{h\cos\alpha-a\sin\alpha}{\sin\alpha}\), so \(d=\frac{h\cos\alpha-a\sin\alpha}{9\sin\alpha}\).
Answer: (3) \(\frac{h\cos\alpha-a\sin\alpha}{9\sin\alpha}\)
Step 2: All poles subtend angle \(\alpha\) at O, so the tops lie on a line through O: \(\tan\alpha=\frac{h}{a+9d}\).
Step 3: \(9d=h\cot\alpha-a=\frac{h\cos\alpha-a\sin\alpha}{\sin\alpha}\), so \(d=\frac{h\cos\alpha-a\sin\alpha}{9\sin\alpha}\).
Answer: (3) \(\frac{h\cos\alpha-a\sin\alpha}{9\sin\alpha}\)
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