PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45$$^\circ $$, 30$$^\circ $$ and 30$$^\circ $$, then the height of the tower (in m) is :

A tower T₁ of height 60 m is located exactly opposite to a tower T₂ of height 80 m on a straight road. Fromthe top of T₁, if the angle of depression of the foot of T₂ is twice the angle of elevation of the top of T₂, then the width (in m) of the road between the feetof the towers T₁ and T₂ is :

An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt 3 $$ kmabove it, is obsered at an elevation of $${60^o}$$ from a point on the ground. If, after five seconds, its elevation from the same point, is $${30^o}$$, then the speed (in km / hr) of the aeroplane, 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: