At a point,$15 \, m$ away from the base of a $15 \, m$ high house,the angle of elevation of the top is (in $^{\circ}$)

$A$ man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^{\circ}$. When he moves $36 \ m$ away from the bank,he finds the angle to be $30^{\circ}$. Find the breadth of the river (in $m$).

From a point $20 \; m$ away from the foot of a tower,the angle of elevation of the top of the tower is $30^{\circ}$. The height of the tower 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?

The angle of elevation of the sun when the length of the shadow of a pole is $\sqrt{3}$ times the height of the pole will be (in $^{\circ}$)

The height of a tower is $100 \text{ m}$. When the angle of elevation of the sun changes from $30^{\circ}$ to $45^{\circ}$,the shadow of the tower becomes $x \text{ m}$ smaller. The value of $x$ is (in $\text{m}$):