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 540 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 370 paces you see an opening through the woods.

Part A

Which direction should you go to reach the treasure?

Part B

How far should you go to reach the treasure?

Explanation / Answer

due North 540 paces ; due east 140 paces

60 deg east of north ; d = 370 paces

X = 370 cos(90 - 60) = 320.43

Y = 370 sin(90 - 60) = 185

The total distance to be travelled

D = sqrt [(140 - 320.43)^2 + (540 - 185)^2] = 398.22 paces

theta = tan-1 (355/-180.43) = -63.1 deg

theta = 63.1 deg North of west (Part A)

D = 398.22 paces (Part B)

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