Question 106408
Jack starting point,0, is the center of a circle and its radius is X km.
I'm assuming that 0 degrees is to the right (East if North is up).
You can re-orient the graph to change that if necessary (North is zero degrees,etc.).
When he changes direction (point A), imagine another center of a circle now with a radius of Y km. 
You are trying to find the point H, on the second circle. 
Set up a grid centered on 0 as (0,0).
When he travels X km on a bearing of 100 degrees, he travels (Xcos(100), Ysin(100)) on the grid. 
{{{drawing( 300, 300, -10, 10, -10, 10,grid( 1 ),green(circle( 0, 0, 6 )),red(line(0,0,-1.04,5.9)),locate(.4,1.2,O),locate(-1.7,7,A))}}}
A new circle is now centered at A. 
He then changes direction and he walks an additional (Ycos(200),Ysin(200))
{{{drawing( 300, 300, -10, 10, -10, 10,grid( 1 ),green(circle( 0, 0, 6 )),red(line(0,0,-1.04,5.9)),locate(.4,1.2,O),locate(-1.7,7,A),green(circle(-1.04,5.9,7)),blue(line(-1.04,5.9,-7.62,3.51)),locate(-7.8,3,H),line(0,0,-7.62,3.51))}}}
His total travel on the x axis is
{{{(DELTA) x=Xcos(100)+Ycos(200)}}}
His total travel on the y axis is
{{{(DELTA) y=Ysin(100)+Ysin(200)}}}
These are also the coordinates of H since you start at (0,0).
{{{(DELTA) x=6(-.174)+7(-.940)}}}
{{{(DELTA) x=(-7.62)}}}
{{{(DELTA) y=6(.984)+7(-.342)}}}
{{{(DELTA) x=(3.51)}}}
H coordinates are (-7.62,3.51)
The vector OH is therefore the vector from (0,0) to (-7.62,3.51)
Magnitude of OH is
{{{OH=abs(sqrt((-7.62-0)^2+(-3.51-0)^2))}}}
{{{OH=8.40}}}
Direction of OH is {{{alpha}}} where
{{{tan(alpha)=-3.51/7.62}}}
{{{alpha=155.3^o}}}
Hopefully these match your answers. 
Good luck.