Sine and Cosine Rule

sine wave
  • The Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles. Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.
  • In ΔABC is an oblique triangle with sides a,b and c. If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle, then to find the sides,you can write as
a /sinA  =   b/sinB  =  c/sinC
Oblique Triangle


cosine wave
  • The Cosine Rule states that the square of the length of any side of a triangle equals the sum of the squares of the length of the other sides minus twice their product multiplied by the cosine of their included angle.
  • The cosine rule expresses the sin2(β) + cos2(β) = 1 relationship for the arbitrary triangle. In symbols:
Cosine Formula

Three further relationships also hold:

  • a = b cos(C) + c cos(B)
  • b = c cos(A) + a cos(C)
  • c = a cos(B) + b cos(A)



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