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.

Calculate the Unknown Sides and Angles of a Triangle

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 1st and 2nd term,

Solving 1st and 3rd term,

Question 2: Solve in which and and .

The Triangle of the PQR

Solution:

Let՚s Calculate the third angle-

Now, Let՚s Calculates the Sides:

approximately.

Similarly,