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{\text{opposite}}{\text{adjacent}} $, we have $ 1 = \frac{h}{100} $. Solving gives $ h = 100 $ meters. Thus, the height of the lighthouse is $\boxed{100}$ meters.

Sun, 03 May 2026 11:52:55 +0000

Content under review