Asked by Cassidy
A man runs 2.7 km north and then 1.3 km in a direction 24° east of north. A woman walks directly between the same initial and final points.What distance does the woman walk? (km) In what direction does the woman walk? (Enter only positive, acute angles.)
Answers
Answered by
oobleck
Draw a diagram!
If we label the points
A: start
B: where he turned
C: final location
Then we have a triangle ABC with angle B = 156°
Now just use the law of cosines to find AC.
relative to B, C is at 1.3sin24° East and 1.3cos24° North
So, from A, C is at (x,y) = (2.7+1.3cos24°,1.3sin24°)
So, relative to due East, the angle z is such that
tan z = y/x
If we label the points
A: start
B: where he turned
C: final location
Then we have a triangle ABC with angle B = 156°
Now just use the law of cosines to find AC.
relative to B, C is at 1.3sin24° East and 1.3cos24° North
So, from A, C is at (x,y) = (2.7+1.3cos24°,1.3sin24°)
So, relative to due East, the angle z is such that
tan z = y/x
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