Physics 2 dimensional vectors Question. Find the end point->Walk 25m due north....

Find the end point->Walk 25m due north, then journey goes 45degrees West of North for 20m. Then you travel 20m due South and finally 10m East of South.
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Apparently there seems o be a trick in the last part

distance from first/initial point, 13.9897, angle, N 30.36 W... not sure but i think this is it

computing the horizontal distance.. since there are two vertical distance given we won't consider it.. so

solving for horizontal(x) distance.. +E and -W
cos(angle) = adjacent/hypotenuse ; x/d
x = d(cos(angle))

10m(cos45)-20m(cos45) = horizontal distance
horizontal dist =-7.07 (negative indicates west)

then for vertical(y) distance .. N+ and S-
sin(angle) = oppsite/hypotenuse ; y/d
y = d(sin(angle))

25m+20m(sin45)-20m-10m(sin45) = vertical distance
vertical dist = 12.07

using pythagorean theorem sq rt of (a^2 + b^2) = c^2

sq rt (12.07^2+7.07^2) = distance
DISTANCE = 13.9897m

for angle with respect to x axis or the horizontal , tan(angle) = opposite/adjacent

(angle) = arctan(opposite/adjacent) ; angle =arctan(y/x)
(angle) = arctan(12.07/7.07)
ANGLE = 59.64 degrees west of north

ps.. i am kinda reckless at times in solving, just correct me if i'm wrong >.<

I've got problems with your "East of South" due to the fact that there is no such direction.

If you meant East BY South, you are referring to a point on the compass 11° 15' south of east
i.e.; 101° 15'.

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Just parse it out with geometry and trig

25 m North puts you at (0,25)

20 m west of north

cos 45 = x/h = x/20
x = 14.14 in the minus direction ===> -14.14
sin 45 = y/h = y/20
y = 14.4 in the + direction ===> + 14.14

That puts you at ( 0 - 14.14, 25 + 14.14) = (- 14.14, 39.14)

South 20 m that is 20 in the - y direction = -20
That puts you at (-14.14, (39.14 - 20)) = (-14.14, -19.14)

10 m East of South (45 degrees?)

cos 45 = x/h = x/10
x = 7.07 in the + x direction => +7.07

sin 45 = y/h = y/10
y = 7.07 in the - y direction = - 7.07

Final position

((-14.14+7.07),(-19.14-707)) ==> (-7.07, - 26.21)

Plot it.
Start at (0,0)..........go 25m north to (25,0)......go 20m north-west to ( 39.14,-14.14).......go 20n south to (19.14, -14.14)...........go 10m south-east to (12.07, -7.07)

You end up at (12.07, -7.07) .

Is "East of South" the same and SE?