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 510 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. (Figure 1)

Part A

Which direction should you go to reach the treasure?

Part B

How far should you go to reach the treasure?

Answer 1

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The treasure map in the figure gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 510 paces, then due east for 150 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 350 paces you see an opening through the woods.(Figure 1)

1)Which direction should you go to reach the treasure?

2How far should you go to reach the treasure?

co-ordnate of treasire = 150 i^ + 510 j^

position of the person after travelling along the wall = 350 * sin 60 i^ + 350*cos 60 j^ = 303.1089 i^ + 175 j^


so vector to be taken to reach the treasure = final position - intial = 150 i^ + 510 j^ - 303.1089 i^ - 175 j^   = -153.1089 i^ + 335 j^

so direction in angle = tan inverse ( 153.1089 / 335 ) = 24.562 degrees west of North


2) distance = sqrt ( 153.1089^2 + 335^2) = 368.3305 paces