Answer:
6.2 km
Step-by-step explanation:
Let x be the distance travel by ship between the two observations of the lighthouse.
AC=3.7 km
[tex]\angle B=34.5^{\circ}[/tex]
[tex]\angle A=37.6^{\circ}[/tex]
In triangle ABC,
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
Triangle angle sum property
Substitute the values
[tex]37.6+34.5+\angle C=180[/tex]
[tex]\angle C=107.9^{\circ}[/tex]
sin law:[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]
Taking [tex]\frac{b}{sin B}=\frac{c}{sin C}[/tex]
Substitute the values then we get
[tex]\frac{3.7}{sin 34.5}=\frac{x}{sin 107.9}[/tex]
[tex]x=\frac{3.7\times sin 107.9}{sin 34.5}[/tex]
[tex]x=6.2 km[/tex]
Hence, the ship travel between the two observations of the light house=6. 2 km
