a boat is traveling with a velocity of 42km\h(40 degree south of east) in a river. The river's current is 5km\h south. what will be the resultant velocity of the boat relative to the shore?

Answer 1

So I assume the 42km/hr is relative to the water?

If it is, relative to shore, you add the vectors
Draw the figure. The angle between the 42 and the 5 is 130 deg (check the figure). Law of Cosines:
speed^2=5^2+42^2 - 2(5)(43)cosine130
do the math

Answer 2

All anglesare measured CW from +y-axis
Vr = 42[130o] + 5[180o].
Vr = (42*sin130+5*sin180) + (42*cos130+5*cos180)I,
Vr = 32.2 - 32i = 45.4km/h[-45.2o] = 45.4km/h[45.2o] E. of S.