Question

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?​

Answer 1

The shipmate must travel 54.48 miles to the south

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:

`sin(\theta) = (lado\ opuesto)/(hipotenusa)`

We know that the angle
`\theta` = 27 °.

So:

`sin(27\°) = (x)/(120)\\\\x = 120sin(27)\\\\x = 54.48\ millas`

The shipmate must travel 54.48 miles to the south