The **Law of Sine is** also known as Sine Formula or Sine Rule in Trigonometry. These rules deal with sides of a triangle with any of its angles. Let’s look at the Sine rule formula.

## Sine Rule Formula

\(\frac{a}{sin A}\) = \(\frac{b}{sin B}\) = \(\frac{c}{Sin C}\) |

Where a, b, c are the lengths of the sides opp to angle A, angle B, and Angle C of the triangle for which we will use the Law of sines.

## Law of Sines Formula Example

**Example**: If angle B = 21^{0}, angle C= 46^{0} and the side AB = 9 cm in a triangle is given. Find the other sides of triangle.

**Solution: **

Given: two angles and a side

Let’s use the Sine rule to solve this.

As the sum of angles in a triangle is 180^{0}

Accordingly, angle A = 113^{0}

As AB = c = 9 cm.

Use the Sine Rule:

\(\large \frac{a}{sin 113^{\circ}}= \frac{b}{sin 21^{\circ}}= \frac{9}{Sin 46^{\circ}}\) \(\large \frac{b}{sin 21^{\circ}} = \frac{9}{sin 46^{\circ}}\)b = sin 21^{0} x 9 /sin 46^{0}

= 4.484 cm

a = sin 113^{0 }x 9 /sin 46^{0}

=11.517 cm.

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