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 470 paces, then due east for 100 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 350 paces you see an opening through the woods. Which direction should you go to reach the treasure? (west of north) How far should you go to reach the treasure? (paces)

Explanation / Answer

Here ,

let east is the positive x direction

north is the positive y direction

let the displacement needed is d

Now, for the same displacement

470 j + 100 i = 350 * (sin(60) i + j * cos(60)) + d

d = -203 i + 295 j m

d = sqrt(203^2 + 295^2) at arctan(203/295) west of north

d = 358 m at 34.5 degree west of north

he should walk at 358 m at 34.5 degree west of north

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