The angle of elevation of the top of a hill from each of the vertices $A, B, C$ of a horizontal triangle is $\alpha$. The height of the hill 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 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 $^{\circ}$)

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:

The angle of elevation of the top of a tower at a point $G$ on the ground is $30^{\circ}$. On walking $20 \ m$ towards the tower,the angle of elevation becomes $60^{\circ}$. The height of the tower is equal to

$A$ person walking along a straight road towards a hill observes at two points,separated by a distance of $\sqrt{3} \text{ km}$,that the angles of elevation of the hill are $30^{\circ}$ and $60^{\circ}$. The height of the hill is