Introduction to Trigonometric Ratios of a Triangle
Trigonometry is all about triangles or to be more precise about the relation between the angles and sides of a rightangled triangle. There are three sides of a triangles named as Hypotenuse, Adjacent, and Opposite. The ratio between these sides based on the angle between them are called Trigonometric Ratios.
As given in the figure in a right angle triangle
 The side opposite to the right angle is called the hypotenuse
 The side opposite to an angle is called the opposite side
 For angle C opposite side is AB
 For angle A opposite side is BC
 The side adjacent to an angle is called the adjacent side

 For angle C adjacent side is BC
 For angle A adjacent side is AB
Trigonometric ratios
There are 6 basic trigonometric relations that form the basics of trigonometry. These 6 trigonometric relations are ratios of all the different possible combinations in a rightangled triangle.
These trigonometric ratios are called
 Sine
 Cosine
 Tangent
 Cosecant
 Secant
 Cotangent
The mathematical symbol θ is used to denote the angle.
A. Sine (sin)
Sine of an angle is defined by the ratio of lengths of sides which is opposite to the angle and the hypotenuse. It is represented as sinθ
B. Cosine (cos)
Cosine of an angle is defined by the ratio of lengths of sides which is adjacent to the angle and the hypotenuse. It is represented as cosθ
C. Tangent(tan)
Tangent of an angle is defined by the ratio of length of sides which is opposite to the angle and the side which is adjacent to the angle. It is represented as tanθ
D. Cosecant(csc)
Cosecant of an angle is defined by the ratio of length of the hypotenuse and the side opposite the angle. It is represented as cscθ
E. Secant(sec)
Secant of an angle is defined by the ratio of length of the hypotenuse and the side and the side adjacent to the angle. It is represented as secθ
F. Cotangent(cot)
Cotangent of an angle is defined by the ratio of length of sides which is adjacent to the angle and the side which is opposite to the angle. It is represented as cotθ.
Trigonometric table
Trigonometric Ratio 
Abbreviation 
Formula 
sine 
sin 
Opposite/Hypotenuse 
cosine 
cos 
Adjacent/Hypotenuse 
tangent 
tan 
Opposite/Adjacent 
cosecant 
csc 
Hypotenuse/Opposite 
secant 
sec 
Hypotenuse/Adjacent 
cotangent 
cot 
Adjacent/Opposite 
Solving for a side in right triangles with trigonometry
This is one of the most basic and useful use of trigonometry using the trigonometric ratios mentioned is to find the length of a side of a rightangled triangle But to do, so we must already know the length of the other two sides or an angle and length of one side.
Steps to follow if one side and one angle are known:
 Choose a trigonometric ratio which contains the given side and the unknown side
 Use algebra to find the unknown side.
Steps to follow if two sides are known:
 Mark the known sides as adjacent, opposite or hypotenuse with respective to anyone of the acute angles in the triangle.
 Decide on which trigonometric ratio can be found out from the above table.
 Find the angle (X)
 Use an trigonometric ratio with respect to X which is a ratio of a known side and an unknown side.
 Use algebra to find the unknown side.