Solution: The angle of elevation is $ 45^\circ $, and the adjacent side (distance from the boat to the base) is 100 meters. Using $ \tan(45^\circ) = \frac\textopposite\textadjacent $, we have $ 1 = \frach100 $. Solving gives $ h = 100 $ meters. Thus, the height of the lighthouse is $\boxed100$ meters. - Groen Casting