Step 1 :Let's denote the distance to the balloon from the closer town as \(d_1\) and the height of the balloon as \(h\). We have \(\tan(39^{\circ}) = \frac{h}{d_1}\).
Step 2 :Similarly, let's denote the distance to the balloon from the farther town as \(d_2\) and the height of the balloon as \(h\). We have \(\tan(35^{\circ}) = \frac{h}{d_2}\).
Step 3 :We also know that \(d_2 = d_1 + 1.5\) miles.
Step 4 :Solving these equations, we find that \(d_1\) is approximately 13.69 miles.
Step 5 :Substituting \(d_1\) into the first equation, we find that the height of the balloon \(h\) is approximately 11.09 miles.
Step 6 :Final Answer: The balloonist is approximately \(\boxed{11.09}\) miles above the ground.