Step 1 :Define the variables h (height) and d (distance).
Step 2 :Set up two equations based on the given information. The first equation is \(h = \tan(32^{\circ}) \cdot d\), and the second equation is \(h = \tan(55^{\circ}) \cdot (d - 200)\).
Step 3 :Solve the system of equations. The solution is \(d \approx 355.58\) and \(h \approx 222.19\).
Step 4 :The solution to the system of equations gives the height of the building as approximately 222.19 feet.
Step 5 :Final Answer: The height of the building is approximately \(\boxed{222.19}\) feet.