The angle of elevation of the top of an unfinished tower at a point $120 \ m$ from its base is $45^{\circ}.$ How much higher (in $m$) must the tower be raised so that its angle of elevation is $60^{\circ}$ at the same point?

The angle of elevation of a ladder leaning against a house is $60^{\circ}$ and the foot of the ladder is $6.5 \ m$ from the house. Find the length of the ladder in metres.

$ABCD$ 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

The angles of elevation of the top of a tower from the points $P$ and $Q,$ at distances of $a$ and $b$ respectively from the base of the tower and in the same straight line with it,are complementary. The height of the tower is

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 $\sqrt{3}$)?

The shadow of a tower standing on a level plane is found to be $50 \ m$ longer when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ} .$ Find the height of the tower. (In $m$)