# Height And Distance – Aptitude MCQ Questions – 06

Question 1

A person, standing exactly midway between two towers, observes the top of the two towers at angle of elevation of 22.5° and 67.5°. What is the ratio of the height of the taller tower to the height of the shorter tower? (Given that tan 22.5° =  √2−1)

 A. 1−2√2 :1 B. 1+2√2 :1 C. 3+2√2 :1 D. 3−2√2 :1

Question 2
When the sun's altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

 A. 35 m B. 140 m C. 60.6 m D. 20.2 m

Question 3
A vertical tower stands on ground and is surmounted by a vertical flagpole of height 18 m. At a point on the ground, the angle of elevation of the bottom and the top of the flagpole are 30° and 60° respectively. What is the height of the tower?

 A. 9 m B. 10.40 m C. 15.57 m D. 12 m

Question 4
From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 200 m high, the distance of point P from the foot of the tower is:

 A. 346 m B. 400 m C. 312 m D. 298 m

Question 5
The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30° respectively. What is the height of the tree?

 A. 22 m B. 44 m C. 33 m D. None of these

Question 6
A ladder 10 m long just reaches the top of a wall and makes an angle of 60° with the wall.Find the distance of the foot of the ladder from the wal (3 =1.73)

 A. 4.32 m B. 17.3 m C. 5 m D. 8.65 m

Question 7
To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and he is 5 m away from the wall, what is the length of the window?

 A. 8.65 m B. 2 m C. 2.5 m D. 3.65 m

Question 8

The angle of elevation of the top of the tower from a point on the ground is sin−1(3/5).  If the point of observation is 20 meters away from the foot of the tower, what is the height of the tower?

 A. 9 m B. 18 m C. 15 m D. 12 m

Question 9
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?

 A. 9 units B. 3√3 units C. Data inadequate D. 12 units

Question 10

An observer 2 m tall is 103 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. 14 m B. 12 m C. 10 m D. None of these