Chapter 3 - Vectors in Physics - Problems and Conceptual Exercises - Page 77: 10

$x=42~ft$

Let h be the vertical distance between the sailor's eye and the top of the lighthouse: $h=49~ft-14~ft=35~ft$ $tan~\theta=\frac{h}{d}$ $d=\frac{h}{tan~\theta}=\frac{35~ft}{tan~30.0°}=61~ft$ This is how far the ship is from the lighthouse. Let x be the distance from the ship to the rocks. $x=61~ft-19~ft=42~ft$