Height and Distance MCQs

A pole 23 m long reaches a window which is $$3\sqrt 5 \,{\text{m}}$$ above the ground on one side of a street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window $${\text{4}}\sqrt {15} \,{\text{m}}$$ high. What is the width (in m) of the street?

Exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 45° and 60°, respectively. The ratio of the heights of P and Q is:

The length of the shadow of a vertical pole on the ground is 36 m. If the angle of elevation of the sun at that time is $$\theta $$ such that $$\sec \theta = \frac{{13}}{{12}},$$ then what is the height (in cm) of the pole?

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 200 m high, the distance between the two ships is:

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is:

From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:

An observer 2 m tall is $$10\sqrt 3 $$  m away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The height of the tower is:

A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30° respectively. What is the height of the poster?

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is: