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a shipmate set aboat to sail excatly 27°ne from the dock. after traveling 120miles, the shipmate realized he had misunderstood the instructions from the captin- he was supposed to set sail going directly east! how many miles will the shipmate have to travel directly south before he is directly east of the dock?​

a shipmate set aboat to sail excatly 27ne from the dock after traveling 120miles the shipmate realized he had misunderstood the instructions from the captin he class=

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carlosego

Answer:

The shipmate must travel 54.48 miles to the south

Step-by-step explanation:

We need to know how many miles south the shipmate traveled. So, we need to find the opposite side of the 27 ° angle shown in the triangle of the attached image.

To find this distance we use the following identity:

[tex]sin(\theta) = \frac{lado\ opuesto}{hipotenusa}[/tex]

We know that the angle [tex]\theta[/tex] = 27 °.

So:

[tex]sin(27\°) = \frac{x}{120}\\\\x = 120sin(27)\\\\x = 54.48\ millas[/tex]

The shipmate must travel 54.48 miles to the south

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