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 500 paces, then due east for 150 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 400 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: (150, 500)

Using the alternate path:
X: 400 cos (90 - 60) = 346.41
Y: 400 sin (90 - 60) = 200

So to reach treasure, you will need to travel a distance of:
D^2 = (150 - 346.41)^2 + (500 - 200)^2
D = 358 paces

Direction:
Tan (theta) = (Y/X)
theta = arctan(Y/X)
theta = arctan(350 / -246.41)
theta = -54.85* or 54.85* North of West

Answer: 358paces; direction: 54.85* North of West

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