It's assumed that the given angles are measured vertically from the top of the light tower.
The angles of elevation for A and B are therefore 90-42°10'=47°50' and 90-47°30'=42°30'.
The height of the tower can be expressed as xtan47°50' and (x+33)tan42°30', where x is the distance from A to the tower.
So xtan47°50'=(x+33)tan42°30'. So x=33tan42°30'/(tan47°50'-tan42°30')=30.2389/0.1878=161 feet approx.