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 520 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 400 paces you see an opening through the woods.

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

2. 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 520 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 400 paces you see an opening through the woods. 1. Which direction should you go to reach the treasure? 2. How far should you go to reach the treasure?

Explanation / Answer

First, find the x and y components of the original and new paths Original path: x = 150 paces, y = 510 paces New path: x = 320cos(60) = 277.128 paces, y = 320sin(60) = 160 paces Next, subtract the original path's components by the new path's components Vx = 150 - 277.128 = -127.128 Vy = 510 - 160 = 350 Then, calculate V V = sqrt[(-127.128)2 + (350)2] = 372.373 Finally, calculate the angle Angle = cos-1(350 / 372.373) = 19.9622 degrees So your answer is an angle of 19.9622 degrees West of North, with a magnitude of 372.373 paces. Hope it helps!

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