Final answer:
The distance between the two mermaids around the outer edge of the island is 2 miles, calculated by finding the arc length of a circle sector with a radius of 6 miles and a central angle of 120 degrees.
Step-by-step explanation:
The problem describes an island with two mermaids spotted from a boat, 120 degrees apart as observed from the boat's position, which is 6 miles away from the island. To find the distance between the mermaids around the island, we need to solve a circle sector problem. The sector's central angle is 120 degrees and we are looking for the arc length of that sector.
To calculate the arc length (L), we use the formula:
L = (r * θ) / (360)
where r is the radius of the circle (6 miles in this case) and θ is the central angle in degrees.
L = (6 miles * 120°) / 360°
L = (720 miles°) / 360°
L = 2 miles
Therefore, the two mermaids are 2 miles apart around the outer edge of the island.