Law of Cosines

Question

Use the Law of Cosines to find angle B if a=4,b=6, and c=9 (Round to 2 decimals places)

 

I don't know if this answer is right but this is what I did

 

cos B = (6^2 - 4^2 - 9^2/-2(4)(9)) = ((36-15-81)/-72) = -61/-72 = .8472222222

 

Then I used my calculator 

 

cos^-1(.847222222)

 

Answer : 

cos B = 32.09

 

Don't know if this is the right answer

Answer 1

cos B = (a² - b² + c² ) / 2ac

cos B = (4² - 6² + 9² ) / (2 · 4 · 9)

cos B = (16 - 36 + 81) / 72

cos B = 61 / 72

cos B ≈ 0.84722

 

B ≈ 32.09

 

Either we are both correct or both wrong! Let's go for both correct!

Answer 2

Carlos,

 

Everything looks right except some notation. You wrote 42 = 15 and that cos(B) = 32.09 degrees, when I think you meant B = 32.09 degrees (especially since cosine is not typically going to return an answer in degrees).

 

cos B = [b² - a² - c²] / [-2ac]

 

cos B = [6² - 4² - 9²] / [-2*4*9]

 

cos B = [36 - 16 - 81] / [-72]

 

cos B = 61/72.

 

arccos (cos B) = arccos (61/72)      Note: arccos(x) is the same thing as cos^-1(x)

 

B ~ 0.56 radians

B = 32.09 degrees