In triangle ABC, if A=63°, b=23m, c=13m Find B, C and a

Question

A=63°, b=23m, c=13m. Find B, C and a.

Answer 1

Given triangle sides are b= 23m, c = 13m and A = 63

To solve the triangle we need to find side a and Angles B,C.

From the law of cosines a^2 = b^2+c^2-2bcCosA

a^2 = (23)^2+(13)^2-2(23)(13)Cos(63)

a^2 = 529+169-598(0.45)

a^2 = 698-269.1

a^2 = 428.9

a = 20.7

From the  law of sines a/SinA = b/SinB = c/SinC

Now we can able to write SinA/a = SinB/b

Sin(63)/20.7 = SinB/23

0.89/20.7 = SinB/23

0.042 = SinB/23

0.988 = SinB

B = Sin^-1(0.988)

B = 81.11

We know sum of angles in a triangle = 180

So 63+81.11+C = 180

C = 180-(63+81)

C = 35.89

Values of C = 36, B = 81, a = 21.