Step 1 :Set up a proportion using the properties of similar triangles: \(\frac{AD}{AC} = \frac{AE}{BC}\)
Step 2 :Plug in the known values and solve for AD: \(\frac{AD}{15} = \frac{26}{30}\) => \(AD = \frac{15 \times 26}{30}\)
Step 3 :Calculate the value of AD: \(AD = \frac{15 \times 26}{30} = 13\)
Step 4 :\(\boxed{13}\)