Right angled triangle and Application of right angled triangle
Right Angled Triangle:
right angled triangle,
ABC with sides
BC = a
CA = b and
AB = c ;
We know that:
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
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.
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.
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 ,
Thus, height of the tower = AC = 51.96 Meters.
- Pythagorian Identities Fundamental Pythagorian identity of trigonometry and other basic trigonometric formulas...
- Trigonometric Functions What are trigonometric functions such as sine , cosine ,...
- Derivatives of Trigonometric functions. As you know, The functions SINE x(sin x) , CO-SECANT...
- Trigonometric functions of negative angles Trigonometric functions of negative angles. How to find trigonometric functions...
- Derivatives of inverse trigonometric functions Inverse trigonometric functions are the inverse of trigonometric functions ....