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.)

Answer 1

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