# Law Of Sines And Cosines Formula

The law of Sine and Cosine also called Sine and Cosine rules are used for finding the solution for the oblique triangle. It is a triangle which is not a right triangle. The angles in this triangle have all acute or only one obtuse.

## The law of Sine (Sine Rule)

There are two cases where we use the Sine Rule

1. AAS or ASA
2. SSA

This rule says that the sides of a given triangle are proportional to the sine of the opposite angles i. e

• p/ Sin P = q / Sin Q , r / Sin R

## The law of Cosine (Cosine Rule)

This rule says that the square of the given length of the side of a triangle is equal to the sum of the squares of the length of other sides minus twice their product and multiplied by the cosine of their included angle.

• p2 = q2 + r2 – 2qr cos P , Cos P = (q2 + r2 – p2) / 2qr
• q2 = p2 + r2 – 2pr cos Q , Cos Q = (p2 + r2 – q2) / 2pr
• r2 = p2 + q2 – 2pq cos R , Cos R = (p2 + q2 – r2) / 2pq

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