What is the measure of ∠F, to the nearest degree? 44° 57° 71° 78°

Three lines given -- it's a natural for the cos(theta) law. A small hint: I think  the preferred way of doing it is to use the cos(theta) law twice. It will give you a definite answer.

Find G first
g = 6 yd
h = 7 yd
f = 5 yards.

g^2 = h^2 + f^2 - 2*h*f*cos(G)
6^2 = 7^2 + 5^2- 2*7*5*cos(G)
36 = 49 + 25 - 70*Cos(G)
36 = 74 - 70*cos(G)
-48 = - 70 * cos(G) Divide by -70
-38/-70 = cos(G)
0.5429 = cos(G)
cos-1(0.5429) = G
G = 57.12

Now find H
h^2 = g^2 + f^2 - 2*g*f*cos(H)
7^2 = 5^2 + 6^2 - 2*5*6*cos(H)
49 = 25 + 36 - 60cos(H)
49 =61  - 60*cos(H) 
Cos(H) = -12 / - 60
Cos(H) = 0.2
H = cos-1(0.2)
H = 78.46

F  can be found because every triangle has 180 degrees
F + 78.46 + 57.12 = 180
F +  135.58 = 180
F = 180 - 135.58
F = 44.41

A <<<< Answer.