Use the angle of depression to find the angle opposite to the distance to the boat (x):
The angle of depression and the angle opposite to the distance to the boat are complementary angles (sum up to 90º)
[tex]\begin{gathered} \alpha+20=90 \\ \alpha=90-20 \\ \alpha=70 \end{gathered}[/tex]
Use the trigonometric ratio of tangent of angle α:
[tex]\begin{gathered} \tan \alpha=\frac{\text{opposite}}{\text{adjacent}} \\ \\ \tan 70=\frac{x}{100ft} \end{gathered}[/tex]
Solve x:
[tex]\begin{gathered} x=100ft\cdot\tan 70 \\ x=274.8ft \end{gathered}[/tex]Then, the distance to the boat is 274.8ft
