I want to make sure I am doing this right (trigonometry question)

While crossing the Atlantic, sailors spot two mermaids 120° apart on each end of an island that is 6 miles away. How far apart are the mermaids around the outer edge of the island to the nearest tenth of a mile?

would it be s=6(2pi/3)

Question

I want to make sure I am doing this right (trigonometry question)

While crossing the Atlantic, sailors spot two mermaids 120° apart on each end of an island that is 6 miles away. How far apart are the mermaids around the outer edge of the island to the nearest tenth of a mile? 

would it be s=6(2pi/3)

mertsj · Answer

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mertsj · Answer

$$s=12\sqrt{3}$$

anonymous · Answer

I'm pretty sure he wants to know how you reached that conclusion.
The question specified that the two mermaids (assuming the sailors wernt just flat out drunk and were just seeing things) were on either side of the island, 120 degrees apart from each other, meaning that each one of them are 60 degrees (half of 120) from the island. The distance between one mermaid and the island, if you draw out the diagram properly, should be s=6*tan(60 degrees)=6tan(pi/3)=6*sqrt(3). The distance between the two mermaids is then simply 2s = 12sqrt(3)

mertsj · Answer

I figured the picture would make that clear.

anonymous · Answer

I suppose. Would still help if you labeled it though.

anonymous · Answer

I followed everything you said until you said s= 6*tan(60 degrees) where and why did you get tan. @CLOUDYskies