theta equals 55 degrees, b = 12, c = 20

Question

Law of Cosine

Answer 1

Given triangle sides are b = 12, c = 20

I assume the given angle A is 55.

In this case to solve triangle we need to find the side a and angles B,C.

Use law of the cosines

a^2 = b^2+c^2-2bc CosA

a^2 = 144+400-480 Cos(55)

a^2 = 544-480(0.5735)

a^2 = 544-275.28

a^2 = 268.72

a = Sqrt(268.72)

a = 16.39

Now we know three sides of triangle,let's find out the remaining angles of triangle.

From the cosine law

CosB = (c^2+a^2-b^2)/2ca

= (400+268.63-144)/655.6

= 524.63/655.6

= 0.8002

B = Cos^-1(0.8002)

B = 36.85

C = 180-(A+B)

C = 180-(55+36.85)

C = 180-91.85

C = 88.15