# 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 22.5Â° and 67.5Â°. What is the ratio of the height of the taller tower to the height of the shorter tower? (Given that tan 22.5Â° =Â  âˆš2âˆ’1)

 Â Â Â A. 1âˆ’2âˆš2 :1 Â Â Â B. 1+2âˆš2 :1 Â Â Â C. 3+2âˆš2 :1 Â Â Â D. 3âˆ’2âˆš2 :1

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

 Â Â Â A. 35 m Â Â Â B. 140 m Â Â Â C. 60.6 m Â Â Â 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 30Â° and 60Â° respectively. What is the height of the tower?

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

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

 Â Â Â A. 346 m Â Â Â B. 400 m Â Â Â C. 312 m Â Â Â 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 60Â° and 30Â° respectively. What is the height of the tree?

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

Question 6
A ladder 10 m long just reaches the top of a wall and makes an angle of 60Â° with the wall.Find the distance of the foot of the ladder from the wal (âˆš3 =1.73)

 Â Â Â A. 4.32 m Â Â Â B. 17.3 m Â Â Â C. 5 m Â Â Â 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 60Â° and 45Â° 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?

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

Question 8

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

 Â Â Â A. 9 m Â Â Â B. 18 m Â Â Â C. 15 m Â Â Â 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 30Âº with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45Âº. What is the distance between the base of the tower and the point P?

 Â Â Â A. 9 units Â Â Â B. 3âˆš3 units Â Â Â C. Data inadequate Â Â Â D. 12 units

Question 10

An observer 2 m tall is 10âˆš3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30Âº. The height of the tower is:

 Â Â Â A. 14 m Â Â Â B. 12 m Â Â Â C. 10 m Â Â Â D. None of these