If a flagstaff of $6 \ m$ high placed on the top of a tower throws a shadow of $2\sqrt{3} \ m$ along the ground,then the angle (in degrees) that the sun makes with the ground is.......$^o$

$AB$ is a vertical pole resting at the end $A$ on the level ground. $P$ is a point on the level ground such that $AP = 3 \, AB$. If $C$ is the mid-point of $AB$ and $CB$ subtends an angle $\beta$ at $P$,the value of $\tan \beta$ is

The sum of angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it is $90^{\circ}$. Then, the height of the tower is

The horizontal distance between a tower and a building is $10 \sqrt{3}$ units. If the angle of depression of the foot of the building from the top of the tower is $60^{\circ}$ and the angle of elevation of the top of the building from the foot of the tower is $30^{\circ}$,then the sum of the heights of the tower and the building is

Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP = 2AB$. If $\angle BPC = \beta$,then $\tan \beta$ is equal to:

From the top of a lighthouse $60 \ m$ high with its base at the sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is: