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 110 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^degree east of north. After walking 340 paces you see an opening through the woods. Which direction should you go to reach the treasure? How far should you go to reach the treasure?

Explanation / Answer

part A)

for the tressure ,

the position of tressure is

d = 470 j + 110 i

let the final displacement needed is d1

d1 + 340 * (sin(60) i + cos(60) j) = 470 j + 110 i

solving for d1

d1 = -184.4 i + 300 j paces

direction he should go = arctan(184.4/300)

direction he should go = 31.6 degree west of north

partr B)

distance he have to walk = sqrt(300^2 + 184.4^2)

distance he have to walk = 352.1 paces

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