CBSE Class 10 Maths Notes Chapter 9- Some Applications of Trigonometry.
Heights and Distances
Horizontal Level and Line of Sight:
The straight line from the eyes of the observer to the subject matter is known as the line of sight. Our eyes move through an angle in this process of creating a line of sight and the angle is known as the "angle of depression". When a situation arises where the object is below the horizontal line. The angle which is created by the line of sight from the horizontal line is known as the angle of depression of an object viewed.
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The horizontal line which is formed through the eyes of the observer is known as the Horizontal level.
In the case when the observer's line of sight is above the horizontal line, The angle formed from the horizontal upward to the object matter is termed the "angle of elevation".
In the real-life world, when we look upward to a building's top while standing on the ground the angle formed from the horizontal is upward to the building which is termed the angle of elevation.
CBSE Class 10 Maths Notes of All Chapters:
CBSE Class 10 Maths Notes Chapter 8 Introduction To Trigonometry
CBSE Class 10 Maths Notes Chapter 10 Circle
In case when the observer's sight is below the horizontal line, the angle formed from the horizontal downward to the object matter is termed the " angle of depression". If we take a real-life example of this, when we look below from the top of a building or from anywhere higher than the ground at an object where you are standing, the angle will be formed downward at the horizontal level, and that angle is known as the angle of depression.
Calculations of Heights and Distances
The calculations of heights and distances can be done with the use of trigonometric ratios.
Step 1: Form a line diagram on the behalf of the problem.
Step 2: Make sure to mark all the known lengths, angles of elevation and angles of depression, and also denote all the unknown heights and distances by "variables"
Step 3: Obtained the unknown lengths with the help of the known lengths with the proper use of the values of various trigonometric ratios.
Become more curious to learn the use of trigonometry in the real world and calculate the heights and distance without struggling to measure them.
In the CBSE Class 10 NCERT based solutions you will also be learning the measurements of the distances of celestial bodies with the use of trigonometry.
The parallax method can be used to measure all the long distances.
When an object is viewed from two different positions the half of the angle between those two lines of sight formed is termed the Parallax angle. Once you understand the concepts of Parallax angle and the distance between two positions from where the object is being viewed, measuring large distances will be easy.
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Frequently Asked Questions:
The joined lines of you standing, the horizontal line and the line which is formed from the eyes of the observer to the object create a right-angled triangle.
And the hypotenuse of that right-angled triangle is known as the line of sight.
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