The treasure map in the figure gives the following directions to the buried trea
ID: 1330601 • Letter: T
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 530 paces, then due east for 130 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 340 paces you see an opening through the woods. (Figure 1)
Which direction should you go to reach the treasure?
How far should you go to reach the treasure?
× Treasure 60° Yellow brick road TreeExplanation / Answer
position of treasure = r1 = 130 i + 530 j
position vector of the person after running away from dragon
r2 = 340*sin60 i + 340*cos60 j
r2 = 294.45 i + 170 j
distance of r2 from the treasure
r = r1 - r2
r = 130i + 530 j - 294.45i - 170 j
r = -164.45i + 360 j
direction = tan^-1(164.45/360) = 24.6 degrees west of north
distance = sqrt(164.45^2+360^2) = 395.8 paces <<------answer
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