How Can You Find the Treasure While Avoiding the Dragon?

[Lamnia]

The treasure map in the figure gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 530 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 degrees east of north. After walking 370 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?

I've made several unsuccessful attempts at this problem.

I believe that this should be a vector subtraction problem.

A = 130i + 530j
B = 370cos60i + 370sin60j

A-B = -55i - (530-185*sqrt3)j

inverse tangent /theta = (-55/-(530-185*sqrt3))
distance = sqrt(55^2 + (530-185*sqrt3)^2)

However, these calculations don't lead to the correct answers.

I'd appreciate any nudges in the right direction so that I might reattempt this problem in the proper fashion.

 

[LowlyPion]

The treasure map in the figure gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 530 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 east of north. After walking 370 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?

I've made several unsuccessful attempts at this problem.

I believe that this should be a vector subtraction problem.

A = 130i + 530j
B = 370cos60i + 370sin60j

A-B = -55i - (530-185*sqrt3)j

inverse tangent /theta = (-55/-(530-185*sqrt3))
distance = sqrt(55^2 + (530-185*sqrt3)^2)

However, these calculations don't lead to the correct answers.

I'd appreciate any nudges in the right direction so that I might reattempt this problem in the proper fashion.

What is the angle east of north?

 

[Lamnia]

I've just edited to include that necessary information. Sorry for the initial exclusion!

 

[lightgrav]

Your 60 degrees is measured from WHAT axis?
if it was zero degrees instead would that be 370 i ?

 

[Lamnia]

According to the diagram accompanying the problem the angle is 60 degrees to the right of the y-axis. So... maybe I should be using 30 degrees as the angle to calculate the i and j components of the displacement along the yellow brick road and subtract that from the displacement of the treasure itself?

 

[lightgrav]

yeah.

don't just assume that every formula [ x= r cos(theta)] will work with the data given,
or that every angle in the problem has to be the "right theta" .