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Use the Law of Cosines to find the missing angle.
Find m∠B, given a = 11, b = 12, and c = 17.

Guest May 10, 2018
edited by Guest  May 10, 2018
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According to the Law of Cosines,

 

b2  =  a2 + c2 - 2ab cos B

                                                          Plug in the given values for  a ,  b , and  c .

122  =  112 + 172 - 2(11)(17) cos B

                                                          Simplify each side of the equation.

144  =  121 + 289 - 374 cos B

 

144  =  410 - 374 cos B

                                                          Subtract  410  from both sides of the equation.

144 - 410  =  -374 cos B

 

-266   =   -374 cos B

                                                          Divide both sides ny  -374 .

-266 / -374   =   cos B

 

133 / 187   =   cos B

                                                          Take the inverse cosine of both sides.

B  =  arccos(133/187)

                                                          Plug in arccos(133/187) into a calculator to get that...

B   ≈   44.665°

hectictar  May 10, 2018

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