How far should you go to reach the treasure?

The treasure map in the figure gives the following directions to the buried treasure: “Start at the old oak tree, walk due north for 550 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 degrees east of north. After walking 400 paces you see an opening through the woods.

IF your problem wants the angle in west of north, do arctan(Y/X) and then take that number and subtract it from 90. For example on this answer you would take the 54.85 and do 90-54.85 to get 35.15 degrees WEST of North!!

Treasure Map Directions

Let due north be positive y-direction
Let due east be positive x-direction
Location that you want to arrive at is: (100, 550)
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 = (100 – 346.41)^2 + (550 – 200)^2
D = 428 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: 428 paces; direction: 54.85* North of West

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