# Mathematics: Law of Sines Formula, Solved Examples of Sines Formula (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Law of Sines Formula

To calculate the unknown sides and angles of a triangle, the Law of Sines formula is used. The ratio of any side to the sine of the angle opposite to that side should be the same for all the sides of the triangle. If two sides are given and two angles of the triangle are given, then the unknown angle can be known using law of sines formula.

The **Law of Sines Formula** is,

### Solved Examples

**Question 1**: In a triangle , the side lengths and The angle opposite to the side A is . Calculate the other unknown angles?

**Solution**:

Given,

The law of sines formula is,

Solving 1^{st} and 2^{nd} term,

Solving 1^{st} and 3^{rd} term,

Question 2: Solve in which and and .

Solution:

Let՚s Calculate the third angle-

Now, Let՚s Calculates the Sides:

approximately.

Similarly,