SOLUTION: a group of backpackers, after three days hiking are 30 km north of their starting position. on the first day they hiked 20km east, on the 2nd day they hiked 30 km in a direction 53

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Question 977365: a group of backpackers, after three days hiking are 30 km north of their starting position. on the first day they hiked 20km east, on the 2nd day they hiked 30 km in a direction 53 degree north of west. use the component method to calculate their displacement on the third day.
I got 40km 37° N of E but I'm not really sure.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

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Let positive x be east, positive y be north.
(20,0)+(30cos%28180-53%29,30sin%28180-53%29)+(x,y)=(0,30)
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X components : 20%2B30cos%28127%29%2Bx=0
x=-20-30cos%28127%29
x=-1.946
Y components : 0%2B30sin%28127%29%2By=30
y=30-30sin%28127%29
y=6.041
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D=sqrt%28x%5E2%2By%5E2%29
D=sqrt%28-1.946%5E2%2B%286.041%29%5E2%29
D=6.35km
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theta=tan%5E%28-1%29%28-6.041%2F1.946%29
theta=tan%5E%28-1%29%28-3.104%29
theta=107.9
17.9 degrees W of N.