**Trigonometric ratios sin cos and tan :**

In the right triangle, we refer to the lengths of the three sides according to how they are placed in relation to the angle **θ**

- The side that is opposite to the right angle is called the Hypotenuse. This is the longest side in a right triangle.
- The side that is opposite to the angle
**θ**is called the Opposite side. - The side that runs alongside the angle
**θ**and which is not the Hypotenuse is called the Adjacent side.

We can form six ratios with the sides of a right triangle.

sin **θ = **Opposite side / Hypotenuse side

cos θ = Adjacent side / Hypotenuse side

tan θ = Opposite side / Adjacent side

cosec θ = Hypotenuse side / Opposite side

sec θ = Hypotenuse side / Adjacent side

cot θ = Adjacent side / Opposite side

**Example 1 :**

Find the cosine ∠C

**Solution :**

Formula to find cos θ is Adjacent side / Hypotenuse side

Here θ has to be considered in the place of ∠C

90° is at ∠A. So the side which is opposite to 90° is known as hypotenuse side. The side which is opposite to θ (∠C) is known as opposite side. The remaining side is known as adjacent side.

BC = hypotenuse side = 17

AB = opposite side = 8

AC = Adjacent side = 15

cos C = 15/17

**Example 2 :**

Find the sin ∠A

**Solution :**

Formula to find sin θ is Opposite side / Hypotenuse side

Here θ has to be considered in the place of ∠A.

AC = hypotenuse side = 65

BC = opposite side = 33

AB = Adjacent side = 56

sin C = 33/65

**Example 3 :**

Find the tan ∠B

**Solution :**

Formula to find tan θ is Opposite side / Adjacent side

Here θ has to be considered in the place of ∠B.

BC = hypotenuse side = 5

AC = opposite side = 4

AB = Adjacent side = 3

tan A = 4/3

After having gone through the stuff given above, we hope that the students would have understood "Trigonometric ratios sin cos and tan".

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