Use the Law of Cosines to find the specified missing value.find C

Question

B = 116°, a = 4.2 ft, c = 6.8 ft,

Answer 1

Hi Sheily, I guess other tutors don't like to work with  the Law of Cosines.

 

b² = a² + c² - 2ac cos B

b² = 4.2² + 6.8² - 2(4.2)(6.8) cos 116°

b² = 17.64 + 46.24 - 57.12 (-.43837)

b² = 63.88 + 25.03969

b² = 88.91969

b = 9.4297

 

Now, you can use the Law of Sines to find angle C.

 

sin C = sin B

   c         b

 

sin C = sin 116°

  6.8      9.43

 

9.43 sin C = 6.8 (sin 116°)

 

sin C = (6.8)(.89879)

                 9.43

 

sin C = .64812

 

C = arcsin (.64812)     remember this is sin raised to the -1 power on calculator

 

C = 40.4°