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 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?

Explanation / Answer

Let due north be positive y-direction
Let due east be positive x-direction

Location that you want to arrive at is: (100, 510)

Using the alternate path:
X: 300 cos (90 - 60) = 259.80
Y: 300 sin (90 - 60) = 150

So to reach treasure, you will need to travel a distance of:
D^2 = (100 - 259.80)^2 + (510 - 150)^2
D = 393 paces

Direction:
Tan (theta) = (Y/X)
theta = arctan(Y/X)
theta = arctan(360 / -159.80)
theta = -66.06* or 66.06* North of West

Answer: 393 paces; direction: 66.06* North of West

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