JEE Mains · Maths · STD 11 - Trigonometrical equations
A vertical pole fixed to the horizontal ground is divided in the ratio \(3: 7\) by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground \(18\, \mathrm{~m}\) away from the base of the pole, then the height of the pole (in \(meters\)) is :
- A \(12 \sqrt{15}\)
- B \(12 \sqrt{10}\)
- C \(8 \sqrt{10}\)
- D \(6 \sqrt{10}\)
Answer & Solution
Correct Answer
(B) \(12 \sqrt{10}\)
Step-by-step Solution
Detailed explanation
Let height of pole \(=10\, \ell\) \(\tan \alpha=\frac{3 \,\ell}{18}=\frac{\ell}{6}\) \(\tan 2 \alpha=\frac{10\, \ell}{18}\) \(\frac{2 \tan \alpha}{1-\tan ^{2} \alpha}=\frac{10\, \ell}{18}\) \(\text { use } \tan \alpha=\frac{\ell}{6} \Rightarrow \ell=\sqrt{\frac{72}{5}}\) height…
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