Answer:
Distance between Karl and Joe is 38.467 m
Solution:
Let us assume that you are at origin
Now, as per the question:
Joe's tent is 19 m away from yours in the direction
north of east.
Now,
Using vector notation for Joe's location, we get:


Now,
Karl's tent is 45 m away from yours and is in the direction
south of east, i.e.,
from the positive x-axis:
Again, using vector notation for Karl's location, we get:


Now, obtain the vector difference between
and
:


Now, the distance between Karl and Joe, d:
|\vec{d}| = |17.01\hat{i} - 34.51\hat{j}|

d = 38.469 m
The distance between Karl's and Joe's tent is: