# Math՚s: Trigonometric Ratios of Some Special Angles: Application of Trigonometry (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Trigonometric Ratios of Some Special Angles

The values of trigonometric ratios of angles and are summarized as follows:

Trig. Ratios | |||||

Not Defined | |||||

Not Defined | |||||

Not Defined | |||||

Not Defined |

Example (i) Find the value of

Solution-

Example (ii) - In , right angled at , if , , find the length of the sides and .

Solution: Given

and

Now,

By Pythagoras Theorem,

## Application of Trigonometry

The Trigonometric ratios are applied to know the distance between the objects or the heights of objects. The following angles are important while solving practical problems on application of trigonometry

### Angle of Elevation

When the observer is looking at an object which is at a greater height than the observer , he has to lift his eyes to see the object and an angle of elevation is formed between the line of sight joining the observer՚s eye to the object and the horizontal line.

### Angle of Depression

When the observer (A) (at a greater height) , is looking at an object (at a lesser height) , the angle formed between the line of sight and the horizontal line is called an angle of depression.

1. A ladder leaning against a window of a house makes an angle of with the ground. If the length of the ladder is , find the distance of the foot of the ladder from the wall.

Solution- Let be a ladder leaning against the wall, making an angle of with the level ground .

Here … (Given)

Now in right angled ,

The distance of the foot of the ladder from the wall is .