Heights & Distances: Class 10 Previous Year Questions

Heights & Distances questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. If a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, prove that the other two sides are divided in the same ratio.
   Board 20235 markslong answerRepeated: 2023,2024,2025
2. From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 45o. The height (in metres) of the tower is : 10 /3 (B) (A) 30 /3 (C) 60 (D) 30
   Board 20261 markMCQ
3. Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in t…
   Board 20264 marksshort answer
4. Tejas is standing at the top of a building and observes a car at an angle of depression of 3o as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to 6o°, and at that moment, the car is 25 m away from…
   Board 20264 markscase-based
5. A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is 10/3 m away from the base of the tower, is : (a) 30° (b)45° (c) 90° (d) 60°
   Board 20261 markMCQ
6. (a) Two ships are sailing in the sea on either side of a lighthouse. The angles of depression to the two ships as observed from the top of the lighthouse are 60 and 45 , respectively. If the distance between the ships is 100 m, then find the height of the ligh…
   Board 20255 markslong answer
7. | P a g e 38. Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be 60 . Then, she climbed a nearby observation deck, 40 metres higher than her original position and noti…
   Board 20254 marksshort answer
8. A pole 6m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point P on the ground is 60° and the angle of depression of the point P from the top of the tower is 45°. Find the height of the tower and the distance…
   Board 20245 markslong answer
9. (a) As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30 and 60 . If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use 3 = 1·73)…
   Board 20235 markslong answer
10. (a) The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 6o. The angle of elevation of the distance between two towers and the height of the other tower. Also, find the length of the wire attached to the to…
    Board 20235 markslong answer
11. (a) The angle of elevation of the top of a building from the foot of the tower is 30 and the angle of elevation of the top of the tower from the foot of the building is 60 . If the tower is 50 m high, then find the height of the building. 3 OR (b) From a point…
    Board 20221 markvery short
12. Heights of 50 students of class X of a school are recorded and following data is obtained : Height 130-135 150-155 135-140 140-145 145-150 155-160 (in cm) : Number of 12 10 11 Students : Find the median height of the students. 11.4 122418
    Board 20221 markvery short
13. In Fig. 3, AB is tower of height 50 m. A man standing on its top, observes two cars on the opposite sides of the tower with angles of depression 30o and 45°respectively.Find thedistancebetweenthetwo cars. 30° 45° 50m Fig. 3 9. (· 25 1 f 1 20 - 30 0- 10 10 - 20…
    Board 20221 markvery short
14. Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14th century. The lake has many Chhatris. One of them is shown below : Observe the picture. From a point A h m above from water …
    Board 20221 markvery short
15. A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change form 30° to 45°, how soon after this, will the car reach the tower? Give your answer to neare…
    CBSE practice 2023-245 markslong answer
16. Answer the following questions based on the given information. The Surya Kiran is an aerobatics demonstration team of the Indian Air Force, and was formed in 1996. In Surya Kiran demonstrations, fighter pilots perform aerobatic maneuvers in groups of 3, to ent…
    CBSE practice 2022-234 marksshort answer
17. Answer the questions based on the given information. A drone, is an aircraft without any human pilot and is controlled by a remote- control device. Its various applications include policing, surveillance, photography, precision agriculture, forest fire monitor…
    CBSE practice 2023-244 marksshort answer
18. A fire engine, standing near a building, extends its ladder to a length of 10 metres to reach a certain window in the building. What is the height of the window from the ground? A. 6 m B. 8 m C. 9 m D. 11 m
    CBSE practice 2021-221 markMCQ

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