DOWNLOAD MOBILE APPLICATION TO LEARN MORE: HEIGHTS AND DISTANCES CLASS 10 ICSE NOTES
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HEIGHTS AND DISTANCES CLASS 10 ICSE NOTES
- A kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60 degree to the horizontal. Find the length of the string to the nearest metres.
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2. A vertical pole stands on the level ground. From a point on the ground, 25 m away from the foot of the pole, the angle of elevation of its top is found to be 60°. Find the height of the pole.
Sol. Let AB be the pole standing on level ground and let O be the position of the observer.
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4. An aeroplane at an altitude of 1500 m finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30°, respectively. Find the distance between the two ships.
Sol. Let the distance between two ships be DC = x m and height of the aero plane from the ground is AB = 1500 m
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5. A man observes the angle of elevation of the top of a building to be 30°. He walks towards it in a horizontal line through its base. On covering 60 m, the angle of elevation changes to 60°. Find the height of the building correct to the nearest metres.
Sol. Let AB be the building of height h m. Initially, the man is at the point C, such that the angle of elevation of the point A is 30°
On walking 60 m, he reaches point D, such that the angle of elevation of the point A is 60°
6. As observed from the top of a 80 m tall light-house, the angles of depression of two ships on the same side of the light-house in horizontal line with its base are 30° and 40°, respectively. Find the distance between the two ships. Give your answer correct to the nearest metres.
Sol. Given, height of a light-house, AB = 80 m.
7. The angle of elevation of an aero plane from a point P on the ground is 60°. After 12 s from the same point P, the angle of elevation of the same plane changes to 30° If the plane is flying horizontally at a speed of
Sol. Let A be the position of plane, when the angle of elevation from point P on the ground is 60°
Distance covered by plane in 12 s
Hence, the height of plane is 3000 m or 3 km.
8. The angle of elevation of a cloud from a point 60° m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud.
Again, let C be the position of the cloud and D be its reflection in the lake.
Let the height of the cloud be Hm.
Then, BC = BD = Hm
9. Two pillars of equal heights stand on either side of a road, which is 150 m wide. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 60° and 30°. Find the height of each pillar and the position of the point on the road.
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10. In the following figure, from the top of a building AB = 60 m high, the angles of depression of the top and bottom of a vertical lamp-post CD are observed to be 30° and 60°, respectively. Find
Sol. (i) Given, height of building AB = 60 m and height of lamp-post is CD. Through point D, draw a horizontal line to meet AB at E
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10th ICSE
| Also Learn: | Attempt theQuiz on Mathematics : | Attempt theQuiz on Physics: | Attempt theQuiz on Biology: | Attempt theQuiz on Chemistry: |
| 1.Surface Areas and Volumes 2. ELECTRICITY 3. METALS AND NON METALS 4. ATOMS AND MOLECULES 5. GST 6. PHOTOSYNTHESIS IN HIGHER PLANTS 7. ABSORPTION BY ROOTS 8. QUADRATIC EQUATIONS 9. LINEAR INEQUATIONS 10. RECURRING DEPOSIT 11. CIRCULAR MOTION 12. MCQ WORK POWER ENERGY 13. ACIDS BASES AND SALTS 14. MCQ ON ACIDS BASES AND SALTS 15. ROTATIONAL MOTION MASS 2 16. ROTATIONAL MOTION MASS 1 17. MCQ ON PERIODIC TABLE 2 18. MCQ ON PERIODIC TABLE 1 19. CELL CYCLE AND CELL DIVISION 20.REFLECTION CLASS 10 ICSE NOTES 21.EQUATION OF LINE CLASS 10 ICSE NOTES 22.CIRCLE CLASS 10 ICSE NOTES 23.SURFACE AREA AND VOLUME CLASS 10 ICSE | QUIZ ON SURFACE AREAS AND VOLUMES- MATHEMATICS QUIZ ON SECTION AND MID-POINT | QUIZ ON ELECTRICITY- PHYSICS | QUIZ 1 ON METALS AND NON-METALS – CHEMISTRY QUIZ 2 ON METALS AND NON-METALS – CHEMISTRY |
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