Class 10 Maths Chapter 9, Some Applications of Trigonometry (Heights and Distances), applies trigonometric ratios of 30°, 45° and 60° to find heights of towers, buildings, statues and lighthouses and distances across rivers and roads without direct measurement.
What Class 10 Maths Chapter 9 Covers
9.1 & 9.2 Heights and Distances defines the line of sight, angle of elevation (when the object viewed is above the horizontal level) and angle of depression (when the object viewed is below the horizontal level, equal to the alternate interior angle of elevation at the ground), and models one-triangle and two-right-triangle problems using tan θ, sin θ and cos θ.
Exercises in Chapter 9
- Exercise 9.1 (15 Questions) solves problems on a circus artist climbing a 20 m rope, a storm-broken tree touching the ground at 30°, park slides for two age groups, kite string length, a tall boy walking towards a 30 m building, a transmission tower on top of a 20 m building, a statue on a pedestal, two poles of equal height on opposite sides of an 80 m road, ships observed from a 75 m lighthouse, and a car approaching a tower at uniform speed.
Read Class 10 Maths Chapter 9 Online
More Chapters
- Previous: Chapter 8: Introduction to Trigonometry
- Next: Chapter 10: Circles
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FAQ
What is the difference between angle of elevation and angle of depression?
The angle of elevation is the angle between the horizontal line and the line of sight when the observer looks upwards at an object above eye level. The angle of depression is the angle between the horizontal line and the line of sight when the observer looks downwards at an object below eye level.
Which trigonometric ratio is most frequently used in Heights and Distances problems?
Tangent (tan θ = Opposite/Adjacent = Height / Horizontal Distance) is used whenever a problem relates the vertical height of an object and its horizontal distance from the observer; sin θ or cos θ is used when the slant length (such as a rope, ladder or kite string) is involved.