The shadow of a tower of height $(1 + \sqrt{3}) \text{ m}$ standing on the ground is found to be $2 \text{ m}$ longer when the sun's elevation is $30^{\circ}$ than when the sun's elevation was $...^{\circ}$.

The angle of depression of a ship from the top of a tower $30 \, m$ high is $60^\circ$. Find the distance of the ship from the base of the tower.

The angle of elevation of the top of a vertical tower from a point $P$ on the horizontal ground was observed to be $\alpha$. After moving a distance $2 \ m$ from $P$ towards the foot of the tower,the angle of elevation changes to $\beta$. Then the height (in metres) of the tower is

Two poles,$AB$ of length $a$ metres and $CD$ of length $a+b$ $(b \neq a)$ metres are erected at the same horizontal level with bases at $B$ and $D$. If $BD=x$ and $\tan \angle ACB = \frac{1}{2}$,then:

An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be $30^\circ$. After $3 \text{ minutes}$,this angle becomes $60^\circ$. After how much more time will the car reach the tree? (in minutes)

$A$ vertical pole of height $h$ stands on a building of height $H$. The angle of elevation of the top of the building from a point on the ground,which is $5$ units away from the foot of the building,is $\alpha$. The pole subtends an angle $\beta$ at the same point on the ground. If $2 \tan \beta \cot \alpha = 1$,then-