Answer:
235 m (3 sf)
Step-by-step explanation:
See attached diagram for a visual representation of the problem, where F is the fishing vessel and b is the distance between the fishing vessel and the base of the lighthouse.
To calculate b we can use the sine rule formula: Â [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
This rule gives the ratio of the sides and angles of a triangle, where A, B, and C are the angles of the triangle and a, b, and c are the sides of the triangle that are opposite to the corresponding angles.
From the diagram and using the sine rule, we can say that:
[tex]\frac{50}{sin12} =\frac{b}{sinB}[/tex]
However, we need with the value of angle B or the length b to proceed with solving this. Â
We can calculate angle B because we know the other 2 angles of the triangle and also know that the sum of the interior angles of a triangle = 180°.
Therefore, B = 180 - 90 - 12 = 78°
Substituting B = 78° into the [tex]\frac{50}{sin12} =\frac{b}{sinB}[/tex]:                        [tex]\frac{50}{sin12} =\frac{b}{sin78}[/tex]
multiplying both sides by sin 78: Â [tex]b=\frac{50}{sin12} \times sin78[/tex]
Therefore, b = 235.2315055... = 235 m (to 3 significant figures)
