Ch:9 Some Application of Trigonometry

SOME APPLICATION OF TRIGONOMETRY

Introduction

The height or length of an object or the distance between two distinct objects can be determined with the help of trigonometric ratios.

Line of Sight and Angle of Elevation

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.

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.

From the above figure, if we want to find the height CD of the pole without actually measuring it, we need the following information:
(i) Distance ED of the observer from the pole.
(ii) the angle of elevation ∠BAC, of the top of the pole.
(iii) 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 ∠BAC or ∠A.
In ∆ABC, the side BC is the opposite side to the known ∠A. Now we use either tan A or cot A, as these trigonometric ratios involve AB and BC to find BC.
Therefore, tan A = BCAB or cot A = ABBC, which on solving would give us BC. By adding AE to BC, you will get the height of the pole.