Find g

Step 1: Recall the cosines formula
The law of cosines is a formula that relates the three sides of a triangle to
the cosine of a given angle
FORMULA: a^2 = b^2 + c^2 - 2bc \cos(A)
b^2 = a^2 + c^2 - 2ac \cos(B)
c^2 = b^2 + a^2 - 2ba \cos(C)
Where each lowercase letter (like a) is the length of the side opposite the
vertex labeled with the same capital letter.
Step 2: Use the cosine formula to find unknown length.
Since you know
The lengths of two sides f = 6
h = 12
The measure of the included angle \angle FGH = 46\degree
Unknown length g = ?
Cosines formula
g^2 = h^2 + f^2 - 2fh \cos 46\degree
g^2 = 12^2 + 6^2 - 2(6*12) \cos 46\degree
g^2 = 144 + 36 - 144 (0.694) (\because use\ calculator\ to\ find\ the\cos46\degree\ value)
g^2 = 79.969
g =8.942