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 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 east of north. After walking 340 paces you see an opening through the woods. (Figure 1)

Which direction should you go to reach the treasure?

How far should you go to reach the treasure?

Explanation / Answer

first the man travels 530 in north direction

then travels 130 paces east

then moves 340 paces 60 degrees east of north

while moving at an angle of 60 degrees he ,moved both in x and y directions,

so, lets break that into components

along north it will be 340cos (theta)=170 m

along east it will be 340* sin(60) =294.44 m

so, now total displacement in north direction is 170 + 530 = 700 paces

total displacement in east direction is 130 +294.44 = 424.44 paces

so, the dispacement to reach the treasure is sqrt( 7002 +424.442) =818.62 paces

the direction is , arc(tan( north /east) = 58.76 degree from the east direction.

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