Physics problem help me please!!!?
A sailor in a small sailboat encounters shifting winds. She sails 2.00km east, then 3.5km southeast, and then an additional distance in an unknown direction. Her final position is 5.80km directly east of the starting point. Find the magnitude and direction of the third leg of the journey. Draw the vector addition diagram and show that it is in qualitative agreement with your numerical solution.
Please help me with this problem. I can't seem to get this one. Please show me step by step what you did to achieve the answer.
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You must break down the second vector into one in the eastern direction, and one in the south direction.
cos(45)*3,5=2,47km in the southern direction.
sin(45)*3,5=2,47km in the eastern direction.
Clearly, the missing vector must be 2,47km north
5.8-2,47-2=1,33km east
length=sqrt(2,47^2+1,33^2)=2,8 km
cos(angle)=1,33/2,8
angle=arccos(1,33/2,8)=61,6 degrees northeast