# Right angled triangle and Application of right angled triangle

**Right Angled Triangle**:

In a

right angled triangle,

ABC with sides

BC = a

CA = b and

AB = c ;

We know that:

or ,

And or ,

And or ,

It is obvious that SIN A = COS B , COS A = SIN B because:

A+B = 90 , So A is the complement angle of B , this may be stated as:

Sine of the angle A = Sine of the complement of B

So , Sine of the angle A = CoSine of angle B

Or ,

And similarly:

and

In a triangle , there are three angles and three sides. They are known as the six components or elements of a triangle.

To solve a triangle means to find unknown elements from the given parts.

It is always possible to solve a triangle if three of it’s parts are given (Except for the case that all three parts given are angles)

In solving problems of practical interest in which right-angled triangles appear , we shall use some new terms. They are “The Point of observation” , “Horizontal” , “Line of Sight” , “Angle of Elevation” , “Angle of Depression”.

These terms are diagrammatically illustrated illustrated below:

**Application Of Right Angled Triangle**:

To solve a real life problem involving right angled triangle , we first collect the given information and then solve the triangle and find the unknown parameters.

For example:

Q. A person 30 meters away from the feet of a tower finds that his line of sight of top of the tower is making an angle of 60 degrees with the horizontal , then find the Height of thee tower.

Solution:

First of all let’s make a visualisation of the situation in diagrammatic form as:

Where , AC is the tower and B is the point from where the person is watching the top of thee tower.

So in the Right Angled triangle ABC ,

Or,

Thus, height of the tower = AC = 51.96 Meters.

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