Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Let a vertical tower $\mathrm{A B}$ of height $\mathrm{2 h}$ stands on a horizontal ground. Let from a point $\mathrm{P}$ on the ground a man can see upto height $\mathrm{h}$ of the tower with an angle of elevation $\mathrm{2 \alpha.}$ When from $\mathrm{P}$ , he moves a distance $\mathrm{d}$ in the direction of $\mathrm{\overrightarrow{A P},}$ he can see the top $\mathrm{ B}$ of the tower with an angle of elevation $\mathrm{ \alpha.}$ If $\mathrm{ d=\sqrt{7} h},$ then $\mathrm{ \tan \alpha}$ is equal to
Option: 1
$\sqrt{5}-2$

Option: 2
$\sqrt{3}-1$

Option: 3
$\sqrt{7}-2$

Option: 4
$\sqrt{7}-\sqrt{3}$

Answers (1)

best_answer

$\mathrm{\tan 2 \alpha=\frac{h}{x}}\\$

$\mathrm{\text { and } \tan \alpha=\frac{2 h}{x+\sqrt{7} h}}\\$

$\mathrm{\tan \alpha=\frac{2 h}{h \cot 2 \alpha+\sqrt{7} h}}\\$

$\mathrm{\tan \alpha=\frac{2}{\frac{\left(1-\tan ^{2} \alpha\right)}{2 \tan \alpha}+\sqrt{7}}}\\$

$\mathrm{\text { Put } \tan \alpha=t\; \& \text { simplify }}\\$

$\mathrm{\Rightarrow \tan \alpha=\sqrt{7}-2}$

Hence correct option is 3

Posted by

manish

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_b of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75

Trending Articles/News

anam-khan

Amrita BTech Admission 2025: JEE Main-based registration deadline extended to August 30

Latest Question