Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

CHAPTER AT A GLANCE

1. Line of Sight and Angle of Elevation:

Suppose we are viewing an object standing on the ground. Clearly, the line of sight ( or line of vision) to the object is the line from our eyes to the object, we are viewing.


In the above figure, the line AC drawn from the eye of an observer at A to the top of the pole ‘C’ is called the line of sight. The observer is looking at the top of the pole. The angle BAC, so formed by the line of sight with the horizontal, is called the angle of elevation of the top of the pole from the eye of an observer.

2. Angle of Depression:


In the above figure, the line AC, is the line of sight as the observer is looking downwards from the top of the building at A towards the object at C. Here angle DAC, so formed by the line of sight with the horizontal, when the observer is lowering his/her head is called Angle of depression.

3. Solving the Problems:


From the above figure, if we want to find the height CD of the pole without actually measuring it, we need the following information:

  • Distance ED of the observer from the pole.
  • the angle of elevation L. BAC, of the top of the pole.
  • the height AE of the observer if it is considerable

Assuming that the above three conditions are known we can determine the height of the pole in the following way.

In the figure, CD= CB+ BD. Here, BD = AE, which is the height of the observer.
To find BC, we will use trigonometric ratios of L. BAC or LA.

In ABC, the side BC is the opposite side to the known L A. Now we use either tan A or cot A, as these trigonometric ratios involve AB and BC to find BC.

Therefore, tanA = BC/AB OR Cot= AB/BC, which on solving would give us BC. By adding AE to BC, you will get the height of the pole.

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