1. Tardigrade
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  4. Let a vertical tower AB of height 2 h stands on a horizontal ground. Let from a point P on the ground a man can see upto height h of the tower with an angle of elevation 2 α. When from P, he moves a distance d in the direction of A P, he can see the top B of the tower with an angle of elevation α. If d=√7 h, then tan α is equal to

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

JEE MainJEE Main 2022Trigonometric Functions

Solution:

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$\tan 2 \alpha=\frac{h}{x}$
and $\tan \alpha=\frac{2 h}{x+\sqrt{7} h}$
$\tan \alpha=\frac{2 h}{h \cot 2 \alpha+\sqrt{7} h}$
$\tan \alpha=\frac{2}{\frac{\left(1-\tan ^2 \alpha\right)}{2 \tan \alpha}+\sqrt{7}}$
Put $\tan \alpha=t \&$ simplify
$\Rightarrow \tan \alpha=\sqrt{7}-2$