Heights and Distances Quiz - CBSE Class 10 Mathematics

Free practice quiz: Heights and Distances (CBSE Class 10 Mathematics). 13 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. A person stands 30 meters away from a tower. If the angle of elevation to the top of the tower is 45°, what is the height of the tower?

   1. 30 meters
   2. 20 meters
   3. 15 meters
   4. 45 meters
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   Answer: A. 30 meters

2. Find the height of a building if a person standing 10 meters away from the base sees the top of the building at an angle of elevation of 60°.

   1. 5√3 meters
   2. 10√3 meters
   3. 10 meters
   4. 15 meters
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   Answer: B. 10√3 meters

3. A cliff is observed from two points A and B on the same horizontal level, with A, B and the foot of the cliff in a straight line and A and B on the same side of the cliff. If the angle of elevation at point A is 30° and at point B is 45°, and the distance between points A and B is 40 m, find the height of the cliff.

   1. 20(√3 + 1) meters
   2. 20(√3 - 1) meters
   3. 20√3 meters
   4. 40√3 meters
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   Answer: A. 20(√3 + 1) meters

   Let C be the foot of the cliff and h its height. From the 45° angle at B, tan 45° = h/BC, so BC = h. From the 30° angle at A, tan 30° = h/AC, so AC = h√3. Since A, B and C are in a straight line and A is farther from the cliff, AC − BC = AB = 40. Thus h√3 − h = 40, giving h = 20(√3 + 1) meters.

4. A man standing on the ground observes the angle of elevation of the top of a 40 meter tall building. If he is 30 meters away from the building, what is the angle of elevation?

   1. 53.13°
   2. 60°
   3. 45°
   4. 30°
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   Answer: A. 53.13°

5. If a 40-meter tall building is observed from a distance of 40 meters, what is the angle of elevation to the top of the building?

   1. 30°
   2. 45°
   3. 60°
   4. 75°
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   Answer: B. 45°

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