The ninth chapter in Mathematics textbook is 'Some Applications of Trigonometry'.
Line of Sight
When an observer looks from a point E (eye) at an object O then the straight line EO between the eye E and the object O is called the line of sight.
Horizontal
When an observer looks from a point E (eye) to another point Q which is horizontal to E, then the straight line, EQ between E and Q is called the horizontal line.
Angle of Elevation
When the eye is below the object, then the observer has to look up from the point E to the object O. The measure of this rotation (angle θ) from the horizontal line is called the angle of elevation.
Angle of Depression
When the eye is above the object, then the observer has to look down from the point E to the object. The horizontal line is now parallel to the ground. The measure of this rotation (angle θ) from the horizontal line is called the angle of depression.
The topics discussed in this chapter are as follows:
- Horizontal Level and Line of Sight
- Angle of elevation
- Angle of depression
- Calculating Heights and Distances
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NCERT Solutions for Chapter 9: Some Applications of Trigonometry
Also Check
Chapter 1: Real Numbers
Chapter 2: Polynomials
Chapter 3: Pair of Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progression
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry
Chapter 10: Circle
Chapter 11: Constructions
Chapter 12: Areas Related to Circles
Chapter 13: Surface Areas and Volume
Chapter 14: Statistics
Chapter 15: Probability
Check out Frequently Asked Questions (FAQs) for Chapter 9: Some Applications of Trigonometry
The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is
Say x is the height of the building.
a is a point 30 m away from the foot of the building.
Here, height is the perpendicular and distance between point a and foot of building is the base.
The angle of elevation formed is 30°.
Hence, tan 30° = perpendicular/base = x/30
1/√3 = x/30
x = 30/√3
From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower (in m) standing straight is
We know:
tan (angle of elevation) = height of tower/its distance from the point
tan 60° = h/15
√3 = h/15
h = 15√3
If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building ___________.
We know, for an angle of elevation θ,
tan θ = Height of building/Distance from the point
If we increase both the value of the angle of elevation remains unchanged.
The angle formed by the line of sight with the horizontal when the point is below the horizontal level is called
Angle of depression
The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called
Angle of elevation