Question

heading due north at 6.00 m/s relative to the water. The local ocean current is 1.53 m/s in a direction 40° north of east. What is the velocity of the ship relative to the earth?
It is the vector sum of the velocity of the ship relative to the water, and the velocity of the water with respect to the land.
V = 6.0m/s[90o] + 1.53m/s[40o]

X = 6.0*Cos90 + 1.5*Cos40 = 0 + 1.15 = 1.15 m/s.

Y = 6*sin90 + 1.5*sin40 = 6 + 0.96 = 6.96 m/s.

Tan A = Y/X = 6.96/1.15 = 6.05.
A = 80.6o.

V = Y/sin A = 6.96/sin80.6 = 7.05 m/s[80.6o]

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