The angle of elevation of a tower from a distance $50 \; m$ from its foot is $30^{\circ}$. The height of the tower is

If $x = a \cos \theta + b \sin \theta$ and $y = b \cos \theta - a \sin \theta,$ then $x^{2} + y^{2}$ is equal to

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

An aeroplane flying at a height of $5000 \; m$ from the ground passes vertically above another aeroplane at an instant. At that instant,the angles of elevation of the two aeroplanes from the same point on the ground are $60^{\circ}$ and $45^{\circ}$ respectively. The vertical distance between the aeroplanes at that instant is:

$A$ tower subtends an angle of $30^{\circ}$ at a point on the same level as the foot of the tower. At a second point,$h \ m$ above the first,the angle of depression of the foot of the tower is $60^{\circ}$. The horizontal distance of the tower from the point is

From an aeroplane vertically over a straight horizontal road,the angles of depression of two consecutive milestones on the opposite sides of the aeroplane are observed to be $30^{\circ}$ and $60^{\circ}$. Find the height in miles of the aeroplane above the road.