i found the speed i need to find the direction?

Question

A child walks due east on the deck of a ship at 3 miles per hour.
The ship is moving north at a speed of 12 miles per hour.

Find the speed and direction of the child relative to the surface of the water.

Answer 1

So we're on the same page, the speed is
sqrt(9+144), which is the magnitude of the resultant vector of the ship speed and the child's speed relative to the ship.
draw a triangle with the base starting at 0 and going to x=3, then go up to the point x=3, y=12. Go back to the origin in a straight line. This forms a right triangle. The angle between the hypotenuse and the x axis is

atan(12/3)
or
76 degrees north of east

j

Answer 2

I'm guessing you want direction in degrees (where 0 is north on the compass).

East is 90 degrees.

You have a triangle and you want the angle where the "opposite" side is 3 and the "adjacent" side is 12. So basically you have tan x = .25.

So x = approximately 14 degrees

Answer 3

It would be the square root of 12^2 + 3^2