The treasure map in the figure gives the following directions to the buried trea

Question

The treasure map in the figure gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 500 paces, then due east for 140 paces. Dig." But when you arrive, you find an angry dragon just north of the tree. To avoid the dragon, you set off along the yellow brick road at an angle 60 east of north. After walking 300 paces you see an opening through the woods. (Figure 1)

Part A

Which direction should you go to reach the treasure?

Part B

How far should you go to reach the treasure?

Explanation / Answer

a)Coordinates of target=140 i + 500 j

Coordinates after walking 300 paces=300Sin 60i+300Cos 60 j=258i+150 j

Displacement required to reach target=(140i-258i)+(500j-150j)=-118i+350j

Direction=Tan^-1(-118/350)=20.6 degrees due west of north.

b)distance=sqrt(350^2+118^2)=369.35 paces

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