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Revision Notes: Height and Distance | Mathematics Class 10 ICSE PDF Download
Important Concepts
- The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.
- The angle of elevation of an object viewed is the angle formed by the line of sight with the horizontal when it is above the horizontal level, i.e., the case when we raise our head to look at the object.
- The angle of depression of an object viewed is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when we lower our head to look at the object
- Pythagoras theorem: In a right triangle, square of the hypotenuse is equal to the sum of the square of the other two sides.
- Angle measured in anticlockwise direction is taken as positive angle.
- Angle measured in clockwise direction is taken as negative angle.
- Some standard values of trigonometric ratios:
The document Revision Notes: Height and Distance | Mathematics Class 10 ICSE is a part of the Class 10 Course Mathematics Class 10 ICSE.
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FAQs on Revision Notes: Height and Distance - Mathematics Class 10 ICSE
| 1. What is the concept of height and distance in mathematics? |  |
Ans. Height and distance refer to the application of trigonometry in determining the height of objects and the distance between objects based on angles of elevation and depression. This concept is commonly used in problems involving right-angled triangles.
| 2. How do you calculate the height of a tree using trigonometry? | |
Ans. To calculate the height of a tree, you can use the angle of elevation from a certain distance. Measure the distance from the base of the tree, and use the tangent function: height = distance × tan(angle of elevation). This will give you the height of the tree.
| 3. What is the difference between angle of elevation and angle of depression? | |
Ans. The angle of elevation is the angle formed between the horizontal line and the line of sight when looking up at an object, while the angle of depression is the angle formed when looking down at an object from a horizontal line. They are complementary in many problems involving height and distance.
| 4. Can you provide a practical example of height and distance problems? | |
Ans. A practical example could involve determining the height of a building. If you stand 50 meters away from the building and find that the angle of elevation to the top is 30 degrees, you can calculate the height using the formula: height = distance × tan(30°), which leads to the height being approximately 25 meters.
| 5. Why is the concept of height and distance important in real-life applications? | |
Ans. The concept of height and distance is crucial in various fields such as architecture, engineering, astronomy, and navigation. It helps professionals determine dimensions, design structures, and calculate distances accurately, ensuring safety and efficiency in their work.
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