The length of the shadow of a tower is $9 \text{ m}$ when the sun's altitude is $30^{\circ}$. What is the height of the tower? (In $m$)

The angle of elevation of an aeroplane from a point on the ground is $60^{\circ}$. After flying for $30$ seconds, the angle of elevation changes to $30^{\circ}$. If the aeroplane is flying at a constant height of $4500 \text{ m}$, what is the speed (in $\text{m/s}$) of the aeroplane (in $\sqrt{3}$)?

$ABCD$ is a rectangle where the ratio of the lengths of $AB$ and $BC$ is $3:2$. If $P$ is the midpoint of $AB$,then the value of $\sin(\angle CPB)$ is

$A$ man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of $45^{\circ}$ with the man's eye when at a distance of $60 \ m$ from the tower. After $5 \ s$,the angle of depression becomes $30^{\circ}$. What is the approximate speed (in $km/hr$) of the boat,assuming that it is running in still water?

The angle of elevation of an aeroplane as observed from a point $30 \ m$ above the transparent water surface of a lake is $30^{\circ}$ and the angle of depression of the image of the aeroplane in the water of the lake is $60^{\circ}$. The height of the aeroplane from the water surface of the lake is (in $m$):

The shadow of a tower standing on a level ground is found to be $40 \ m$ longer when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ}$. Find the length of the tower. (In $m$)