In this section, you will learn how to find the values of the trigonometric ratios sin, cosine and tangent.

The formulas given below can be used to find the trigonometric ratios sin, cos and tan.

sin **θ = **Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

**Example 1 :**

Find the value of cos C.

**Solution :**

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

So, we have

BC = Hypotenuse = 17

AB = Opposite side = 8

AC = Adjacent side = 15

Then,

cos C = Adjacent side / Hypotenuse

cos C = AC/BC

cos C = 15/17

**Example 2 :**

Find the vale of sin A.

**Solution :**

90° is at ∠B. So the side which is opposite to 90° is known as hypotenuse. The side which is opposite to ∠A is known as opposite side. The remaining side is known as adjacent side.

So, we have

AC = Hypotenuse = 65

BC = Opposite side = 33

AB = Adjacent side = 56

Then,

sin A = Opposite side / Hypotenuse

sin A = BC/AC

sin A = 33/65

**Example 3 :**

Find the value of tan B.

**Solution :**

90° is at ∠A. So the side which is opposite to 90° is known as hypotenuse. The side which is opposite to ∠B is known as opposite side. The remaining side is known as adjacent side.

So, we have

BC = Hypotenuse = 5

AC = Opposite side = 4

AB = Adjacent side = 3

Then,

tan B = Opposite side / Adjacent side

tan B = AC/AB

tan B = 4/3

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