The treasure map in the figure gives the following directions to the buried trea
ID: 1276113 • Letter: T
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 480 paces, then due east for 120 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 350 paces you see an opening through the woods.
A) Which direction should you go to reach the treasure?
B)How far should you go to reach the treasure?
Figure 1of 1 × Treasure 60° Yellow brick road TreeExplanation / Answer
Let due north be positive y-direction
Let due east be positive x-direction
Location that you want to arrive at is: (120, 480)
Using the alternate path:
X: 350 cos (90 - 60) = 303.1
Y: 350 sin (90 - 60) = 175
So to reach treasure, you will need to travel a distance of:
D^2 = (120 - 303.1)^2 + (480 - 175)^2
D = 355.73 paces
Direction:
Tan (theta) = (Y/X)
theta = arctan(Y/X)
theta = arctan(305 / -183.1)
theta = -59.02* or 59.02* North of West
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.