Right Triangles Trigonometry

In a Right Triangle the side opposite to the Right Angle is called the hypotenuse and side opposite to the angle is opposite side and other side is adjacent side.
 
 
Fig:-  Right triangle, right angled at ‘C’.
 
Trigonometry is a branch of mathematics in which we study Triangles and relationships between their sides and the angles between these sides.
The three primary Functions used in right triangle Trigonometry are:
1. Sine abbreviated as sin.
2. Cosine abbreviated as cos.
3. Tangent abbreviated as tan.
 
In Right Triangles Trigonometry, the value for the sine of angle ‘A’ is defined as the value that we get after dividing opposite side by the hypotenuse, i.e.
 
Sin A = opposite side / hypotenuse
         = a/c
 
The value for the cosine of angle ‘A’ is defined as the value that we get after dividing adjacent side by the hypotenuse, i.e.
 
Cos A = adjacent side / hypotenuse,
          = b/c,
The value for the Tangent of angle ‘A’ is defined as the value that we get after dividing the opposite side by the adjacent side, i.e.
Tan A = opposite side / adjacent.
          = a/b.
To remember the formulas, we can learn the following statement
“oh heck, another hour of Algebra!”
Here,
o = opposite side
h = hypotenuse
a = adjacent side
 
First letter represent the formula of the function
 
oh heck,                         sin A = o/h,
another hour                  cos A = a/h,
of algebra                      tan A = o/a,
Using right triangles and trigonometry we can solve many problems, let's take an example.
Suppose we have to find the length of side “a” in the given right triangle ABC if angle ‘A’ is 35°, and side ‘c’ is 10 inch.
 
As angle ‘A’ is 36°, then angle B is 90° − 35° = 55°.
To find side we use the formula,
sin A = opposite side / hypotenuse
=> sin 35 = a / 10,
=> 0.5735 = a / 10 (as sin 35= 0.5735),
=> a = 5.735 inch.