Height and Distance

Total Questions: 45

11. From a point exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 30 and 60 respectively. The ratio of the height of P to that of Q is: [SSC CGL Tier II (12/09/2019)]

Correct Answer: (a) 1 : 3
Solution:

12. The angle of elevation of a flying drone from a point on the ground is 60°. After flying for 5 seconds the angle of elevation drops to 30°. If the drone is flying horizontally at a constant height of 1000√3 m the distance (in m) travelled by the drone is: [SSC CPO 16/03/2019 (Afternoon)]

Correct Answer: (a) 2000
Solution:

13. At a certain time of a day a tree 5.4 m height casts a shadow of 9 m. If a pole casts a shadow of 13.5 m at the same time, the height of the pole is: [SSC CPO 16/03/2019 (Morning)]

Correct Answer: (a) 8.1 m
Solution:

14. What is the angle of elevation of the sun from the top of a pillar, when its height is equal to the length of its shadow? [SSC CPO 15/03/2019 (Evening)]

Correct Answer: (c) 45°
Solution:

15. The top of a broken tree touches the ground at a 60° angle, 45 meters away from the root of the tree. What will be the total height (in m) of the tree? [SSC CPO 14/03/2019 (Evening)]

(Use √3 = 1.73 and √2 = 1.41)

Correct Answer: (c) 167.85
Solution:

16. From the top of the 120 m high lighthouse, the angle of depression of two ships on opposite sides of the base of the lighthouse is 30° and 60°. What is the distance between the ships? (rounded off) [SSC CPO 14/03/2019 (Morning)]

Correct Answer: (c) 277 m
Solution:

17. From the top of 75 m high tower, the angle of depression of two points P and Q on opposite side of the base of the tower on level ground is θ and Φ, such that tanθ = 3/4 and tanΦ = 5/8. What is the distance (in m) between the points P and Q? [SSC CPO 13/03/2019 (Morning)]

Correct Answer: (d) 220
Solution:

18. From the top of a 12 m high building, the angle of elevation of the top of the tower is 60° and the angle of depression of the foot of the tower is θ, such that tanθ = 3/4. what is the height of the tower ? (√3 = 1.73) [SSC CPO 12/03/2019 (Evening)]

Correct Answer: (c) 39.68
Solution:

19. A ladder leaning against a wall makes an angle alpha with the horizontal ground such that tan α = 3/4. If the foot of the ladder is 5m away from the wall, what is the length (in m) of the ladder ? [SSC CPO 12/03/2019 (Morning)]

Correct Answer: (c) 6.25
Solution:

20. A pole 10 m long rests slantly against a vertical wall AB making an angle 30° with the horizontal (ground). Find how far the foot of the pole is from the wall (in metres) [SSCC CGL 10/09/2024 (1st Shift)]

Correct Answer: (d) 5√3
Solution: