Explanation:
30m North
20m East
and the 30
2
SW can be rewritten as 30m in south and 30m in West
because south and west being at 90
0
result
in
30
+30
=30
so at last we have following data that in south X
S
=30m+north=30m+(−30m)=0,
negative becasue north is opposite to south.
and in West we have X
W
=30m+east=30m+(−20m)=10m
so the displacement is 10m due west
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Answers & Comments
You need not make it very complex, you can solve it using simple Pythagorean Theorem,
Sum of Square of Sides = Square of Hypotenuse
Simply draw a diagram of the path taken by the person.

We nee AD,
At C, he turned South West, so it would be 45 Degrees to the current path of Travel, And It would normally intersect AB at 45 Degrees.
Now in Triangle BCE
We know Angle C is 45, and Angle E is 45 as Angle B is 90 (180–90–45)
As Angles E and C are 45, that implies, sides CB and BE are also identical in length. 20 kms. And say Side CE = a
==> a^2 = 20^2 + 20^2
==> a = 20√2
As we know, CD = 30√2
==>ED = CD-CE = 30√2 - 20√2 = 10√2
Now in Triangle ADE, ED = 10√2 and AE = (30–20) = 10
And we know Angle A = 90
S0,
DE^2 = AE^2 + AD^2
==> (10√2)^2 = 10^2 + AD^2
==> AD = Sqrt(200–100) = 10 Kms
Good Luck
Explanation:
30m North
20m East
and the 30
2
SW can be rewritten as 30m in south and 30m in West
because south and west being at 90
0
result
in
30
2
+30
2
=30
2
so at last we have following data that in south X
S
=30m+north=30m+(−30m)=0,
negative becasue north is opposite to south.
and in West we have X
W
=30m+east=30m+(−20m)=10m
so the displacement is 10m due west