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 490 paces, then due east for 100 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? 60 degree east of north. After walking 330 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

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

Location that you want to arrive at is: (100 490)

Using the alternate path:
X: 330 cos (90 - 60) = 285.79
Y: 330 sin (90 - 60) = 165

So to reach treasure, you will need to travel a distance of:
D^2 = (100 - 285.79)^2 + (490 - 165)^2
D = 374.3 paces

Direction:
Tan (theta) = (Y/X)
theta = arctan(Y/X)
theta = arctan(325 / -185.79)
theta = -60.24* or 60.24* North of West

Answer: 374.3 paces; direction: 60.24* North of West

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