Height and Distance

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min. for the angle of depression of the car to change from 30^o to 45^o ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is :

Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC subtends an angle 30^o at B. The height (in m) of the lamp-post is -

A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB(=a)$ subtends an angle of ${60^ \circ }$ at the foot of the tower, and the angle of elevation of the top of the tower from $A$ or $B$ is ${30^ \circ }$. The height of the tower is :

$AB$ is a vertical pole with $B$ at the ground level and $A$ at the top. $A$ man finds that the angle of elevation of the point $A$ from a certain point $C$ on the ground is ${60^ \circ }$. He moves away from the pole along the line $BC$ to a point $D$ such that $CD=7$ m. From $D$ the angle of elevation of the point $A$ is ${45^ \circ }$. Then the height of the pole is :

$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC \bot CD.$ If $\angle ADB = \theta ,\,BC = p$ and $CD = q,$ then AB is equal to:

A bird is sitting on the top of a vertical pole $20$ m high and its elevation from a point $O$ on the ground is ${45^ \circ }$. It files off horizontally straight away from the point $O$. After one second, the elevation of the bird from $O$ is reduced to ${30^ \circ }$. Then the speed (in m/s) of the bird is :

If the angles of elevation of the top of a tower from three collinear points $A, B$ and $C,$ on a line leading to the foot of the tower, are ${30^ \circ }$, ${45^ \circ }$ and ${60^ \circ }$ respectively, then the ratio, $AB:BC,$ is :

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 :

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30^o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60^o. Then the time taken (in minutes) by him, from B to reach the pillar, is :