A river flows towards the East at 2 m/s. The relative velocity of a fish with the water is 4 m/s towards the north.If the fish faces the same...

The vector that represents the velocity of the river is
added to the vector that represents the relative velocity of fish to river's
velocity.

These two vectors are perpendicular and they are
the legs of the right angle triangle, whose hypotenuse is the resultant of addition of
the vectors. The horizontal leg is the velocity of river and the vertical leg is the
velocity of fish.

The magnitude of horizontal vector is 2
and the magnitude of vertical leg is 4.

The angle that has
to be calculated is made by the hypotenuse to the horizontal
leg.

tan x = vertical leg/horizontal
leg

tan x = 4/2

tan x = 2
=> x = arctan 2 => x = 63.4
degrees.

The requested angle is x = 63.4
degrees.