Height and Distance

Total Questions: 45

1. A man looks at the reflection of the top of the lamp-post on the mirror that is 6.6 m away from the foot of the lamppost. The man's height is 1.25 m and he is standing 2 m away from the mirror. Assuming that the mirror is placed on the ground, facing the sky and the man, and that the mirror and the lamp-post are in a same line, find the height of the lamp-post (in metres). [SSC CHSL 04/07/2024 (1st Shift)]

Correct Answer: (d) 4.13
Solution:

2. The shadow of a tower standing on level ground is found to be 40 m longer when the Sun's altitude is 30° than when it was 45°. Find the height (in meters) of the tower. [SSC CHSL Tier II 10/01/2024 ]

Correct Answer: (c) 20(√3 + 1)
Solution:

3. Two pillars of equal height stand on either side of a roadways which is 150m wide. At a point in the road between pillars, the elevations of the pillars are xº and yº so that tanxº = 2/5, tanyº = 3/5, then the height of each pillar is: [SSC CGL Tier II (26/10/2023)]

Correct Answer: (b) 36m
Solution:

4. Subhas, a 3.15 m tall tree, and an 11.25 m tall building are positioned such that their feet on the ground are collinear and the tree is located between Subhas and the building. The tree is located at a distance of 7.5 m from Subhas and at a distance of 45 m from the building. Further, the eyes of Subhas, the top of the tree, and the top of the building fall in one line. Find the height (in m) from the ground at which Subhas' eyes are situated. [SSC CHSL 09/08/2023 (4th Shift)]

Correct Answer: (b) 1.8
Solution:

5. From the top of an upright pole 17.75 m high, the angle of elevation of the top of an upright tower was 60 deg If the tower was 57.75 m tall, how far away (in m) from the foot of the pole was the foot of the tower? [SSC CGL Tier II (03/03/2023)]

Correct Answer: (d)
Solution:

6. A pole 23 m long reaches a window which is 3√5 m above the ground on one side of a street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window 4√15 m high. What is the width (in m) of the street? [SSC CGL 11/04/2021 (Afternoon)]

Correct Answer: (c) 39
Solution:

So, width of street  = 22 + 17 = 39m

7. 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 way 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 20m and it is 60m away from him. How tall (in m) is the mall? [SSC CPO 25/11/2020 (Morning)]

Correct Answer: (a) 405
Solution:

8. A ladder leaning against a wall makes an θ with the horizontal ground such that If the height of the cos θ = 5/13. If the height of the top of the ladder from the wall is 18m, then what is the distance (in cm) of the foot of the ladder from the wall? [SSC CPO 23/11/2020 (Morning)]

Correct Answer: (c) 7.5
Solution:

9. A pole stands vertically on a road, which goes in the north-south direction. P, Q are two points towards the north of the pole, such that PQ = b and the angles of elevation of the top of the pole at P, Q are α , β respectively. Then the height of the pole is: [SSC CPO 09/12/2019 (Morning)]

Correct Answer: (b)
Solution:

10. A clock tower stands at the crossing Of two roads which point in the north-south and the east-west directions. P,Q,R and S are points on the roads due north, east, south and west respectively, where the angles of elevation of the top of the tower are respectively, α, β, γ and ℘. Then (PQ/RS)² is equal to: [SSC CPO 09/12/2019 (Morning)]

Correct Answer: (c)
Solution: