Right Triangle Trigonometry Math Example 4

Solution

1. 1
   Step 1: Set up the right triangle. The lighthouse height is the opposite side (50 m). The horizontal distance from the base to the boat is the adjacent side. The angle of depression from the top equals the angle of elevation from the boat, which is $32°$.
2. 2
   Step 2: Use $\tan 32° = \frac{\text{opp}}{\text{adj}} = \frac{50}{d}$, where $d$ is the horizontal distance.
3. 3
   Step 3: Solve: $d = \frac{50}{\tan 32°} = \frac{50}{0.6249} \approx 80$ meters.