I don't understand why the law of sines involves tangent?

We don't need to use the law of sines here, since it is a right triangle.

Remember, in a right triangle... tan θ  =  opposite / adjacent

Let's call the distance (in miles) from the boat to the dock  " d ".

tan 52°  =  d / 30       Multiply both sides by  30 .

30 tan 52°  =  d        

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