The Law of Sines

Law of Sines or Sine Rule is helpful for solving the unknown side of an oblique triangle or angle. It contains all the three sides of a triangle corresponding to their sides and angles.

These lows perform for all types of triangles. The sine rule should run with at least two angles and its corresponding side lengths at a time.

In the triangle, three sides are given below:

1.  a
2.  b
3.  c

In the triangle, three angles are also given below:

1. A
2. B
3. C

How Do We Use Law of Sines?

See below some  examples related it:

Q 1. Find the unknown side b and side  c is 6

Solution:

As we know the Law of Sines: a/sin A = b/sin B = c/sin C

put the given values:  b/sin A = b/sin(45°) = 6/sin(70°)

b = c sin B / sin C

b = ( c / sin(70°) ) × sin(45°)

Calculate: c = (6 × 1)/ sin70° × √2

b = (6 x 1)/ 0.905 x 1.414

therefore √2 = 1.414

b = 6 / 1.274

b = 4.69