Answer:
Ship 2
Step-by-step explanation:
From inspection of the diagram, the problem has been modeled as a right triangle. Therefore, to find [tex]x[/tex] and [tex]y[/tex], use trigonometric ratios then compare to determine which distance is the smallest.
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
To find [tex]x[/tex] use the sine trig ratio:
[tex]\implies \sf \sin(\theta)=\dfrac{O}{H}[/tex]
[tex]\implies \sin(47^{\circ})=\dfrac{x}{6}[/tex]
[tex]\implies x=6 \sin(47^{\circ})[/tex]
[tex]\implies x=4.39 \: \sf miles \:(2\:dp)[/tex]
To find [tex]y[/tex] use the cosine trig ratio:
[tex]\implies \sf \cos(\theta)=\dfrac{A}{H}[/tex]
[tex]\implies \cos(47^{\circ})=\dfrac{y}{6}[/tex]
[tex]\implies y=6 \cos(47^{\circ})[/tex]
[tex]\implies y=4.09 \: \sf miles \: (2 \: dp)[/tex]
As 4.09 < 4.39, ship 2 is currently closer to the coast guard.
