+120 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?
+130071 Assuming that the center of the island is "dead ahead," we have a triangle with a height of 6 mi, and assuming that the mermaids were an equal distance from the center of this island, this triangle is isosceles with an apex angle of 120 degrees. And the base of this triangle is their distance from each other.....and the height of the triangle bisects this 120 degrees....so we actually have two congruent 30-60-90 triangles formed by this bi-section........the distance from one mermaid to the center of this island is opposite the 60 degree angle in one of these triangles and the distance to the island - 6 miles - is opposite the 30 degree angle......so...the distance that one mermaid is from the center of the island = the base of one of these 30-60-90 triangles = 6√3 miles
So....the total distance between them = 2*6√3 miles = 12√3 miles = about 20.8 mi.
