# 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 ; right angled triangle

We know that: $\sin A = \dfrac{a}{c}$ or , $a = c \sin A$

And $\cos A = \dfrac{b}{c}$ or , $b = c \cos A$

And $\tan A = \dfrac{a}{b}$ or , $a = b \tan A$

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 , $\sin A = \sin (90-B) = \cos B$

And similarly: $\csc A = \sec B$ and $\tan A = \cot B$

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: application of right angled triangle

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 , $\tan 60 = \dfrac{AC}{BC} = \dfrac{AC}{30}$

Or, $AC = \tan 60 \times 30 = \sqrt{3} \times 30 = 51.96$

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

Related posts:

1. Pythagorian Identities Fundamental Pythagorian identity of trigonometry and other basic trigonometric formulas...
2. Trigonometric Functions What are trigonometric functions such as sine , cosine ,...
3. Derivatives of Trigonometric functions. As you know, The functions SINE x(sin x) , CO-SECANT...
4. Trigonometric functions of negative angles Trigonometric functions of negative angles. How to find trigonometric functions...
5. Derivatives of inverse trigonometric functions Inverse trigonometric functions  are the  inverse of trigonometric functions ....