Solve the triangle?

Question

Side A = 46 degrees

Side C and B = unknown

b = 4

c = 8

a = unknown

Answer 1

Use the Law of Cosines to find the length of side a:

 

     a² = b² + c² - 2bc cos(A)          where b = 4, c = 8, A = 46^o

 

Once you have the length of side a, use the Law of Sines to find angles B and C:

 

     sin(A)/a = sin(B)/b

     b*sin(A)/a = sin(B)

     arcsin(b*sin(A)/a) = B          

 

     sin(A)/a = sin(C)/c

     arcsin(c*sin(A)/a) = C

Answer 2

a^2=b^2+c^2-2bccosA

a^2=16+64-64cos46º

a^2=80-64cos46º

a^2=80-64(0.69465837)

a^2=80-44.45813568

a^2=35.54186432

a=5.961699

 

c^2=a^2+b^2-2abcosC

64=35.54186432+16-8(5.961699)cosC

64=51.54186432-47cosC

12.45813568=-47.693592cosC

12.45813568/(-47.693592)=cosC

-0.261212377=cosC

using arccos

C=105.14201247º (round as you like)

A+B+C=180º

46+B+105.14201247=180º

151.14201247+B=180

180-151.14201247=B

B=28.857987º  (round as you like)