Question 1198572
<font color=black size=3>
x = distance between the two lighthouses
A & B = the two lighthouses
C = location of the ship
D = helper point to label the upper-most red angle
*[illustration Screenshot_156.png]
The diagram was made with GeoGebra.


The red angles are given. 
The blue angle is computed like this:
(angle DAC)+(angle CAB) = 180
angle CAB = 180 - (angle DAC)
angle CAB = 180 - (129°43’)
angle CAB = 179°60’ - (129°43’)
angle CAB = (179°-129°)+(60’-43’)
angle CAB = 50°17’


Then notice how
(angle CAB)+(angle CBA) = (50°17’)+(39°43’)
(angle CAB)+(angle CBA) = (50°+39°)+(17’+43’)
(angle CAB)+(angle CBA) = 89°60’ 
(angle CAB)+(angle CBA) = 90°
Which shows that triangle ABC is a right triangle. The 90 degree angle is located at point C.


This allows us to use the trig ratio sine to say
sin(angle) = opposite/hypotenuse
sin(angle ABC) = AC/AB
sin(39°43’) = 3742/x
sin(39+43/60) = 3742/x
sin(39.716667) = 3742/x


I'll let you finish up.
Make sure your calculator is in degree mode.
</font>