# Height And Distance – Aptitude MCQ Questions – 04

Question 1
The height of a tower is 100 m. When the angle of elevation of the sun changes from 30Â° to 45Â°, the shadow of the tower becomes x metres less. The value of x is

 Â Â Â A. 100m Â Â Â B. 100âˆš3 m Â Â Â C. 100(âˆš3âˆ’1)m Â Â Â D. 100/âˆš3 m

Question 2

The ratio of the length of a rod and its shadow is 1 : âˆš3 Â The angle of elevation of the sum is

 Â Â Â A. 30Â° Â Â Â B. 45Â° Â Â Â C. 60Â° Â Â Â D. 90Â°

Question 3
The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30Â° with horizontal, then the length of the wire is

 Â Â Â A. 12 m Â Â Â B. 10 m Â Â Â C. 8 m Â Â Â D. 6 m

Question 4
A lower subtends an angle of 30Â° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60Â°. The height of the tower is

 Â Â Â A. h/2 m Â Â Â B. âˆš3 h m Â Â Â C. h/3 m Â Â Â D. h/âˆš3 m

Question 5
The tops of two poles of height 16 m and 10 m are connected by a wire of length l metres. If the wire makes an angle of 30Â° with the horizontal, then l =

 Â Â Â A. 26 Â Â Â B. 16 Â Â Â C. 12 Â Â Â D. 10

Question 6

A ladder makes an angle of 60Â° with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is

 Â Â Â A. 4/âˆš3 Â Â Â B. 4âˆš3 Â Â Â C. 2âˆš2 Â Â Â D. 4

Question 7
If the altitude of the sun is at 60?, then the height of the vertical tower that will cast a shadow of length 30 m is

 Â Â Â A. 30âˆš3 m Â Â Â B. 15m Â Â Â C. 30/âˆš3 m Â Â Â D. 15âˆš2 m

Question 8
The angle of elevation of the top of a tower standing on a horizontal plane from a point A is Î±. After walking a distance 'd' towards the foot of the tower the angle of elevation is found to be Î². The height of the tower is

 Â Â Â A. d/cotÎ±+cotÎ² Â Â Â B. d/cotÎ±âˆ’cotÎ² Â Â Â C. d/tanÎ²âˆ’tantÎ± Â Â Â D. d/tanÎ²+tantÎ±

Question 9
The angle of depression of a car parked on the road from the top of a 150 m high tower is 30Â°. The distance of the car from the tower (in metres) is

 Â Â Â A. 50âˆš3 Â Â Â B. 150âˆš3 Â Â Â C. 100âˆš3 Â Â Â D. 75

Question 10
It is found that on walking x metres towards a chimney in a horizontal line through its base, the elevation of its top changes from 30Â° to 60Â° . The height of the chimney is

 Â Â Â A. 3âˆš2 x Â Â Â B. 2âˆš3 x Â Â Â C. âˆš3/2x Â Â Â D. âˆš2/3x