Question 945549
Let east be positive x, west negative x, north positive y and south negative y.
Start at (0,0).
4 miles north
(0,0)+(0,4)=(0,4)
6 miles east
(0,4)+(6,0)=(6,4)
10 miles southeast 
(6,4)+(10cos(225),10sin(225))=(6,4)+(-7.07,-7.07)=(-1.07,-3.07)
So now use the distance formula,
{{{D^2=(-1.07-0)^2+(-3.07-0)^2}}}
{{{D^2=1.1449+9.431458}}}
{{{D^2=10.57864}}}
{{{D=3.25}}}{{{miles}}}