#### Answer

The distance between the two lighthouses is $5856~m$

#### Work Step by Step

The angle in the triangle at lighthouse A is $180^{\circ}-129^{\circ}43'$ which is $50^{\circ}17'$
Let $d$ be the distance between the two lighthouses. Note that $d$ is the hypotenuse of the triangle. We can find $d$:
$\frac{3742~m}{d} = cos~50^{\circ}17'$
$d = \frac{3742~m}{cos~50^{\circ}17'}$
$d = 5856~m$
The distance between the two lighthouses is $5856~m$