Height and Distance MCQs

As observed from the top a light house, 120√3 m above the sea level, the angle of depression of a ship sailing towards it changes from 30° to 60°. The distance travelled by the during the period of observation is:

From the top of hill 240 m high, the angles the angles of depression of the top and bottom of a pole are 30° and 60°, respectively. The difference (in m) between the height of the pole and its distance from the hill is:

A person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a ways that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree height is 20 m and it is 60 m away from him. How tall (in m) is the mall?

The distance between two parallel poles is 40√3 m. The angle of depression of the top of the second pole when seen from the top of first pole is 30°. What will be the height of second tower if the first pole is 100 m long

A ladder is resting against a wall, the angle between the foot of the ladder and the wall is 45° and the foot of the ladder is 6.6 m away from the wall. The length of the ladder (in m) is:

P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are 60° and 30°, respectively and the distance between them is 84√3 m. What is the height (in m) of the pole?

A ladder is placed along a wall such that its upper end is touching the top of the wall. The foot of the ladder is 10 ft away from the wall and the ladder is making an angle of 60° with the ground. When a man starts climbing on it, it slips and now ladder makes an angle of 30° with ground. How much did the ladder slip?

From the top of a 12 m high building, The angle of elevation of the top of a tower is 60° and the angle of depression of the foot of the tower is θ. Such that tan θ = $$\frac{3}{4}$$, what is the height of the tower (√3 = 1.73)?

A poster is on top of a building. A person 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 200% of the height (in cm) of the poster?