This is a perfect place to apply the Law of Cosines. We want angle Z and know the length of the side opposite this angle: 9.7.
Law of Cosines is c^2 = a^2 + b^2 - 2ab*cos C
Applied here, we get
9.7^2 = 6.8^2 + 14.7^2 - 2(6.8)(14.7)*cos Z
Then
94.09 = 46.24 + 216.09 - 199.92*cos Z
Grouping the constant terms together:
-167.43 = -199.92*cos Z
Solving for cos Z:
0-.8374 = -cos Z
0.8374 = cos Z
Applying the inverse cosine function: Z = 0.578 radians = 33 degrees
