# Math's: Trigonometric Ratios: Finding Triangle Sides by Trigonometric Ratios

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## Trigonometric Ratios of an Acute Angle of a Right Triangle

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

### Sides of a Right Triangle

The side opposite to the right angle is called HYPOTENUSE.

The side opposite to the reference angle is called PERPENDICULAR.

The side adjacent to the reference angle is BASE.

**The six trigonometric ratios are:**

## Finding Trigonometric Ratios when Two Sides of a Right Triangle Are Given

To find Trigonometric ratios when two sides of a right triangle are given-

Step1: Use Pythagoras Theorem to find the unknown (third) side of the triangle.

Step 2: Use t-ratios formulae and substitute the values of the sides.

Example 1- In , , and . Find the values of , and .

Solution- By Pythagoras Theorem,

## Relationship between Trigonometric Ratios

## Trigonometric Identities

When the equation involving a variable is true for all values of the variable, it is called an identity. Trigonometric Identities are equations that involve trigonometric ratios and are true for right angled triangles.

The trigonometric identities are-

## Method to Solve Questions on Trigonometric Identities

**Step 1:**Choose from or , which is easier to simplify.**Step 2:**Use different identities to simplify the and arrive at the result on the other hand side.**Step 3:**If you don’t get the result on arrive at an appropriate result and then simplify the other side to get the result already obtained.**Step 4:**As both sides of the identity have been proved to be equal the identity is established.

Example- Prove that

Solution-