Use the Law of Cosines to determine the indicated angle thet

Use the Law of Cosines to determine the indicated angle theta. (Assume a = 67.01, b = 38.41, and c = 42.85.) Solve triangle ABC. (Round the length to three decimal places and the angles to one decimal place.) C = A = B =

Solution

3)

by law of cosines

cos=(a²+c²-b²)_/2ac

cos=(67.01²+42.85²-38.41²)_{/(2*67.01*42.85)}

cos=0.8447

=32.36^o

--------------------------------------------------------------------------------

4)

by law of cosines

c²=a²+b²-2abcosC

c²=15²+11²-2*15*11*cos120^o

c²=511

c=22.605

A=cos^-1[(b²+c²-a²)_/2bc]

A=cos^-1[(11²+22.6053²-15²)_{/2*11*22.3053}]

A=cos^-1[0.81839]

A=35.1^o

B=cos^-1[(a²+c²-b²)_/2ac]

B=cos^-1[(15²+22.6053²-11²)_{/2*15*22.3053}]

B=cos^-1[0.9068666]

B=24.9^o