Finding Resultant of Displacements Using Unit Vectors

[roam]

Homework Statement

A golfer takes three putts to get the ball into the hole of a level putting green. The first putt displaces the ball 2.5 m North, the second 4.8 m South-East and the third 5.7 m South-West.

Express each of these three displacements in unit vector notation where i is a unit vector pointing due East and j is a unit vector pointing due North.

E.g the first displacement is: $$(0)i, (2.5)j$$

The Attempt at a Solution

The first one is obvious but the other two aren't. For example for the second part the question says it is 4.8 m South-East BUT it doesn't say how many degrees due South-East. Without the angle, it is impossible for me to find the rectangular components (i.e $$4.8 sin(\theta), 4.8 cos(\theta)$$). Any suggestions?

 

[rl.bhat]

When they say south of east or south of west the angle is always 45 degrees with east-west line.

 

[roam]

Oh thanks! I found the three displacements in unit vector notation:

$$0i, 2.5j$$
$$3.39i, -3.39j$$
$$-4.03i, -4.03j$$

The question then asks:

Determine the angle in degrees (measured with respect to anticlockwise rotation from an axis pointing due East of the hole) to get the ball into the hole in a single putt.

What do I need to do to answer this problem? I'm a little confused...

 

[rl.bhat]

Find the resultant of these three vectors.
Then tanθ = y/x