Joe's boat leaves the harbor and heads straight for Treasure Island, which is 37 degrees North of West. Joe travels 26 km to reach the island. Moe leaves a little while later and first heads North to try and get a glimpse of some dolphins (that had earlier been sighted by her friends). Moe travels 11 km due North and reaches Nomans island. At this point she is disappointed at having seen no dolphins and heads straight for Treasure Island. What is the distance traveled by Moe from Nomans island to Treasure island?

18.44km

Explanation:

The diagram explains better.

From the diagram,

A is the harbor;

B is Treasure Island;

C is Nomans land.

Using cosine rule, we can find the distance between C and B.

BC² = AB² + AC² - 2*AB*AC*cos(A)

AB = 26km

AC = 11km

A = 37°

BC² = 26² + 11² - (2*26*11*cos37)

BC² = 676 + 121 - (572*0.7986)

BC² = 797 - 456.8

BC² = 340.2

BC = 18.44 km

The distance traveled by Moe from Nomans land to Treasure Island is 18.44km

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