Question

A motorboat is headed [W35ºN] with its engine set to move the boat at 25 km/h in still water. The current is flowing at 18 km/h [S]. What is the velocity of the boat relative to the shore?

My work:

cos(35º)=x/25
25cos35=x
x=20km/h

I have an issue with finding the direction. It is supposed to be [W11ºS]

Answer 1

If you draw the diagram, since 25 sin35º = 14, then the angle θ south of W is

tanθ = (18-14)/20 = 4/20
θ = 11.3º

Answer 2

boat components
... W ... 25 cos(35º) = 20
... N ... 25 sin(35º) = 14

add the boat components to the current

(14 N + 18 S) + 20 W = 20
... the tan of the angle is ... S/W
... arctan(4/20) = 11º ... [W11ºS]