The answer is 14.6
===============================================
Work Shown:
Let x = length of HK
Check out the attached diagram. The given angles are
H = 52
K = 73
So the missing angle J can be found with the equation below
H+J+K = 180
52+J+73 = 180
52+73+J = 180
125+J = 180
125+J-125 = 180-125
J = 55
Use the law of sines to find x.
Make sure your calculator is in degree mode.
HK/sin(J) = JK/sin(H)
x/sin(55) = 14/sin(52)
x = sin(55)*(14/sin(52))
x = 14.5532641116333
x = 14.6 which is the answer we want
Note: only one value is possible for length HK as there is only one unique triangle (due to the AAS congruence theorem)
So we don't have to worry about any ambiguous cases.