Question

PLS HELP!!!

The coast guard is out to sea and gets notification that two ships need help. One ship is directly west of the coast guard, and the other is directly south, as shown in the image below. The two ships are 6 miles from each other. Which ship is currently closer to the coast guard?

PLEASE INCLUDE EXPLANATION!!!! THANK YOU!!!

Answer 1

So

• cos47=Base/Hypotenuse
• cos47=y/6
• y=6cos47

And

• sin47=x/6
• x=6sin47

sin47=0.73

cos47=0.68

So meanwhile sin is greater so 6sin is also greater

• x is greater
• ship 2 is closer

Answer 2

Ship 2

Explanation:

From inspection of the diagram, the problem has been modeled as a right triangle. Therefore, to find
`x` and
`y`, use trigonometric ratios then compare to determine which distance is the smallest.

Trigonometric ratios

`\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)`

where:

• 
  `\theta` 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
`x` use the sine trig ratio:

`\implies \sf \sin(\theta)=(O)/(H)`

`\implies \sin(47^(\circ))=(x)/(6)`

`\implies x=6 \sin(47^(\circ))`

`\implies x=4.39 \: \sf miles \:(2\:dp)`

To find
`y` use the cosine trig ratio:

`\implies \sf \cos(\theta)=(A)/(H)`

`\implies \cos(47^(\circ))=(y)/(6)`

`\implies y=6 \cos(47^(\circ))`

`\implies y=4.09 \: \sf miles \: (2 \: dp)`

As 4.09 < 4.39, ship 2 is currently closer to the coast guard.