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

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Practise This Question

The following pictographs give us the number of guests visited Pratik's house for last 4 days. On which day, no. of guests were maximum? On this day, how many more guests came as compared to the previous day?