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
- AAS or ASA
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 P , Cos P = (p2 + r2 – q2) / 2pr
- r2 = p2 + q2 – 2pq cos P , Cos P = (p2 + q2 – r2) / 2pq
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