Answer
The distance to the boat is approximately 845 feet.
Work Step by Step
We can express the angle in degrees:
$\theta = 2^{\circ}10' = (2 + \frac{10}{60})^{\circ} = 2.17^{\circ}$
We can convert the angle to radians:
$\theta = (2.17^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 0.03787~rad$
Let $h$ be the height of the mast. We can approximate the distance $d$ to the boat:
$h \approx \theta ~d$
$d \approx \frac{h}{\theta}$
$d \approx \frac{32~ft}{0.03787~rad}$
$d \approx 845~ft$
The distance to the boat is approximately 845 feet.
