Applications Of Trigonometry

Trigonometry is the branch of mathematics which deals with Triangles and the relationship between the angles and sides of triangles.
Now we will see some applications of Trigonometry:
Some of the Applications of Trigonometry are given below:
Sine law – The law of sine (is also known as sine law, sine formula, or sine rule) is an equation which is used to compare the length of the sides of a triangle to its angle:
According to the sine law,
 ,
where x, y, and z are the length of the sides of a triangle, and X, Y, and Z are the opposite angles of a triangle.
And the reciprocal of above equation is:

Another application of trigonometry is:
Law of cosines: It is also said to be cosine formula or cosine rule. It is used to compare the lengths of the sides of a triangle to the cosine of one of its angle.
In the mathematical notation the cosine laws says that:
Z² = x² + y² – 2xy cos ∂;
 ‘∂’ represents the angle between sides of lengths ‘x’ and ‘y’ and the opposite side length ‘z’.
Some other trigonometry applications are:
Suppose in a triangle if we know the two angles and one side of a triangle then SAA or ASA or laws of sine can be used to solve the triangle.
Now we will see how to find one side of a triangle:
Suppose we have a triangle XYZ and if X = 33 degree and ‘Y’ is 82.8 degree and ‘x’ is 43.9 inch. Then we find the value of ‘y’.
We know that the law of sine is:
   
Putting the values in the formula, we get:
   
or
Y =