Sine Rule: The sides of a triangle are proportional to the sines of the angles opposite to them.
a / sin A = b / sin B = c / sin C = 2R
(Or)
sin A /a = sin B /b = sin C/c = 1/2R
Where R is the circum radius of the circle.
Ex: If R = 3, a = 6 Then ∟A =?
a = 2Rsin A => 6 = 6 sin A
=> sin A = 1 => ∟A = 90⁰
Cosine Rule: The angle of a triangle are related to three sides of a triangle by cosine rule.
cos A = b2 + c2 – a2 / 2bc (or) a2 = b2 + c2 – 2bc cos A
cos B = a2 + c2 – b2 / 2ac (or) b2 = c2 + a2 – 2ac cos B
cos C = a2 + b2 – c2 / 2ab (or) c2 = a2 + b2 – 2ab cos C
Ex: If a2 + b2 = c2 find cos C?
Sol: cos C = a2 + b2 – c2 / 2ab = 0/ 2ab = 0 => ∟C = 900