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
\(\begin{array}{l}\frac{a}{sin A}\end{array} \) = \(\begin{array}{l}\frac{b}{sin B}\end{array} \) = \(\begin{array}{l}\frac{c}{Sin C}\end{array} \) |
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:
\(\begin{array}{l}\large \frac{a}{sin 113^{\circ}}= \frac{b}{sin 21^{\circ}}= \frac{9}{Sin 46^{\circ}}\end{array} \)
\(\begin{array}{l}\large \frac{b}{sin 21^{\circ}} = \frac{9}{sin 46^{\circ}}\end{array} \)
b = sin 210 x 9 /sin 460
= 4.484 cm
a = sin 1130 x 9 /sin 460
=11.517 cm.
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