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

\begin{array}{l} \frac{a}{s i n A} \end{array}

\begin{array}{l} \frac{b}{s i n B} \end{array}

\begin{array}{l} \frac{c}{S i n C} \end{array}

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 = 21⁰, angle C= 46⁰ 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 180⁰

Accordingly, angle A = 113⁰

As AB = c = 9 cm.

Use the Sine Rule:

\begin{array}{l} \frac{a}{s i n 113^{\circ}} = \frac{b}{s i n 21^{\circ}} = \frac{9}{S i n 46^{\circ}} \end{array}

\begin{array}{l} \frac{b}{s i n 21^{\circ}} = \frac{9}{s i n 46^{\circ}} \end{array}

b = sin 21⁰ x 9 /sin 46⁰

= 4.484 cm

a = sin 113⁰x 9 /sin 46⁰

=11.517 cm.

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Sine Rule Formula

Law of Sines Formula Example

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