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:

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45^o. The angle of elevation of the top of the same tower from a point B, due south of A is 30^o. If the distance between A and B is $$54\sqrt 2 \,m,$$ then the height of the tower (in metres), is :