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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Heights and Distances

NTA Abhyas 2020 · Mathematics · Heights and Distances

Let 10 vertical poles standing at equal distances on a straight...

Let 1010 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α\alpha at a point OO on this line and all the poles are on the same side of OO. If the height of the longest pole is hh and the distance of the foot of the smallest pole from OO is aa; then the distance between two consecutive poles, isLet 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point

Options

  1. A\dfrac{hsin\alpha + a\text\cos\alpha}{9cos\alpha}
  2. Bhcosα−asinα9sinα\dfrac{hcos\alpha - asin\alpha}{9sin\alpha}
  3. C\dfrac{hsin\alpha + a\text\cos\alpha}{9sin\alpha}
  4. D\dfrac{hcos\alpha - a\text\sin\alpha}{9cos\alpha}

Correct answer

B. hcosα−asinα9sinα\dfrac{hcos\alpha - asin\alpha}{9sin\alpha}

Step-by-step solution


Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point

from diagram

tanα=ha+9btan \alpha = \dfrac{h}{a + 9b}

a+9b=hcosαsinαa + 9b = \dfrac{hcos \alpha}{sin \alpha}

9b=hcosα−asinαsinα9b = \dfrac{hcos \alpha - asin \alpha}{sin \alpha}

b=hcosα−asinα9sinαb = \dfrac{hcos \alpha - asin \alpha}{9sin \alpha}
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