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 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 360 paces you see an opening through the woods. Which direction should you go to reach the treasure? Figure 1) Submit My Answers Give Up Incorrect; Try Again; 24 attempts remaining Part B , Figure 1 'of1 How far should you go to reach the treasure? X-... Treasure paces Submit My Answers Sive Up 60 Yellow brick road Provde Feed Tree

Explanation / Answer

Let due north be positive y-direction

Let due east be positive x-direction

Location that you want to arrive at is: (130, 540)

Using the alternate path:

X: 360 cos (90 - 60) = 311.77

Y: 360 sin (90 - 60) = 180

So to reach treasure, you will need to travel a distance of:

D^2 = (130 - 311.77)^2 + (540 - 180)^2

D = sqrt(162640.33) = 403.29 paces

Direction:

Tan (theta) = (Y/X)

theta = arctan(Y/X)

theta = arctan(180 / -311.77)

theta = -29.99 or 29.99 deg North of West

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