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# 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

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.

## The Ratios of Sides

Ratio is defined as a comparison between any two Numbers of same identities that represents the presence of one entity with respect to other. That means it shows how much quantity of one entity is present in comparison with the other entity. It can also be termed as relationship between two entities or identities of same type. It is represented by “a:b” ...Read More

## Definition of the Trigonometric Functions of an Acute Angle

Before going to discuss the definition of the Trigonometric Functions of an Acute Angle let's know about acute angle. An acute angle is an angle which is always lesser than 90 degrees. It does not include 90 degrees anyways. In order to find Trigonometry functions we need an acute angled triangle. And the triangle must be a Rig...Read More

## Solutions of Right Triangles

Solving right Triangles means we need to find the measures of other two angles (as one angle is of 900) or the measures of sides of the Right Triangle.
Figure shown below is a right triangle, right angled at ‘...Read More

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