$ABCD$ 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

From the top of a tower of height $108 \; m$,the angles of depression of two objects on either side of the tower are $30^{\circ}$ and $45^{\circ}$. The distance between the objects is:

An observer on the top of a cliff,$200 \, m$ above the sea level,observes the angle of depression of two ships at anchor to be $45^{\circ}$ and $30^{\circ}$ respectively. Find the distance (in $m$) between the ships if the line joining them stretches to the base of the cliff.

The angle of elevation of a ladder leaning against a wall is $45^{\circ},$ and the foot of the ladder is $4.242 \ m$ away from the wall. The length of the ladder is (in $m$):

Two posts are $2 \text{ m}$ apart. Both posts are on the same side of a tree. If the angles of depression of these posts when observed from the top of the tree are $45^{\circ}$ and $60^{\circ}$ respectively,then the height of the tree is:

$A$ man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes $12$ minutes for the angle of depression to change from $30^{\circ}$ to $45^{\circ},$ how soon after this will the car reach the observation tower?