In the figure ab equals how many inches ac equals how many inches

Remark 
This is a trig question. You need two function (Tan(C) and Cos(C)

Tan(C)
this will give you the value for BA
Tan(C) = BA / BC

Givens
C = 40 degrees
BC = 10
tan(C) = AB/BC
Tan(40) = AB / 10
0.8391 = AB / 10 Multiply both sides by 10
10*0.8391 = AB
AB = 8.391 

Cos(C)
Cos(C) = BC/AC
BC = 10
C = 40 degrees.
Cos(C) = 0.76604
0.76604 = 10/AC     Multiply both sides by AC
0.76604 * AC = 10
AC = 10/0.76604
AC = 13.054