Answer:
27.19°
Step-by-step explanation:
According to the picture attached, we can find the distance between the two vectors using cosine law
[tex]a^{2} =b^{2} +c^{2} -2ab*cosA\\a=\sqrt{b^{2} +c^{2} -2ab*cosA} \\\\a=\sqrt{2.1^{2} +8.9^{2} -2(2.1)(8.9)*cos21}\\a=6.98\\\\[/tex]
Then we can get C angle by applying one more time cosine law between a and b
[tex]c^{2} =a^{2} +b^{2} -2ab*cosC\\\\c^{2} -a^{2} -b^{2}= -2ab*cosC\\\\\frac{c^{2} -a^{2} -b^{2}}{-2ab}=cosC\\ \\CosC=\frac{8.9^{2} -6.98^{2} -2.1^{2}}{-2*6.98*2.1}\\ \\CosC=-0.89\\\\ArcCos(-0.89)=C\\\\C=152.81[/tex]
We can see that the C angle is complement of the angle we are looking for, so we take away 180 degrees to get the answer
[tex]180=C+?\\\\180-C=?\\\\180-152.81=C\\\\27.19=C[/tex]
27.19 degrees is our answer!
