Answer:
The distance from the ship to the dock is approximately 5.24 miles
Step-by-step explanation:
From the parameters given in the question, we have;
The angle formed between the dock and the lighthouse = 70°
The angle formed between the dock and the lighthouse at the ship = 80°
The distance between dock and the lighthouse = 5 miles (From a similar question online)
By sine rule, we have;
[tex]\dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} = \dfrac{c}{sin(C)}[/tex]
Therefore, we have;
[tex]\dfrac{5}{sin(70^{\circ})} = \dfrac{The \ distance \ from \ the \ ship \ to \ the \ dock}{sin(80^{\circ})}[/tex]
[tex]\therefore The \ distance \ from \ the \ ship \ to \ the \ dock = sin(80^{\circ}) \times \dfrac{5}{sin(70^{\circ})}[/tex]
[tex]sin(80^{\circ}) \times \dfrac{5}{sin(70^{\circ})} \approx 5.24 \ mi[/tex]
Therefore;
The distance from the ship to the dock ≈ 5.24 miles
