9. Some Applications of Trigonometry

9. Some Applications of Trigonometry

  • 9

    Some Applications Of Trigonometry

    This section explores practical applications of trigonometry, particularly in measuring heights and distances.

  • 9.1

    Heights And Distances

    This section covers the practical applications of trigonometry in measuring heights and distances using angles of elevation and depression.

  • 9.1.1

    Example 1

    This section presents a problem involving the calculation of the height of a tower using trigonometric principles.

  • 9.1.2

    Example 2

    The section illustrates how to calculate the length of a ladder required for an electrician to reach a specific height safely.

  • 9.1.3

    Example 3

    This section illustrates how to calculate the height of a chimney using trigonometry based on the observer's position and angle of elevation.

  • 9.1.4

    Example 4

    This section involves calculating the height of a flagstaff and the distance from a point to a building using trigonometric relationships.

  • 9.1.5

    Example 5

    This section presents a problem involving the relationship between the height of a tower and the lengths of its shadow at different sun altitudes.

  • 9.1.6

    Example 6

    This section explores the angles of depression from the top of a multi-storeyed building to an 8 m tall building, using trigonometry to determine the height of the multi-storeyed building and the distance between the two.

  • 9.1.7

    Example 7

    This section involves calculating the width of a river using angles of depression from a bridge.

  • 9.1.8

    Exercise 8

    This section presents several exercises involving the calculation of heights and distances using trigonometric principles.

  • 9.2

    Summary

    This section reviews essential concepts related to the line of sight, angles of elevation, and angles of depression in trigonometry.

    • Key Summary

    Trigonometry plays a vital role in determining heights and distances in various real-life applications. The chapter introduces concepts like line of sight, angles of elevation, and angles of depression, providing a foundation for solving practical problems using trigonometric ratios. Through several examples and exercises, the chapter illustrates how these concepts can be applied effectively to calculate unknown heights and distances.

    Key Takeaways

    • The line of sight is drawn from the eye of an observer to the point in the object viewed.
    • The angle of elevation is formed when the line of sight is raised above the horizontal level.
    • The angle of depression is formed when the line of sight is lowered below the horizontal level.
    • Trigonometric ratios assist in determining distances, heights, and lengths of objects.

    Key Concepts

    • Line of Sight: The line drawn from an observer's eye to a point of interest in an object.
    • Angle of Elevation: The angle formed by the line of sight with the horizontal when the observed point is above the horizontal level.
    • Angle of Depression: The angle formed by the line of sight with the horizontal when the observed point is below the horizontal level.
    • Trigonometric Ratios: Ratios such as sine, cosine, and tangent that relate the angles and lengths of triangles, used for calculating heights and distances.