From the given picture, we see that two sides and one angle is given
Using them we have to find the value of angle C
side AB=c=14 in
side BC=a=18 in
angle A= 110 degree
Now plug these values into sine formula
[tex] \frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)} [/tex]
or [tex] \frac{18}{\sin(110)}=\frac{b}{\sin(B)}=\frac{14}{\sin(C)} [/tex]
or [tex] \frac{18}{\sin(110)} =\frac{14}{\sin(C)} [/tex]
or [tex] \frac{18}{0.93969262} =\frac{14}{\sin(C)} [/tex]
or [tex] 19.1551999206=\frac{14}{\sin(C)} [/tex]
or [tex] \sin(C)=\frac{14}{19.1551999206} [/tex]
or [tex] \sin(C)=0.730872037777 [/tex]
or [tex] C=\sin^{-1} (0.730872037777} [/tex]
C=46.959549954213535880191108778655
Which is approx 47 degree.
Hence final answer is C=47 degree.
