You are camping with two friends, joe and karl. since all three of you like your privacy, you don't pitch your tents close together. joe's tent is 19.0 m from yours, in the direction 19.0° north of east. karl's tent is 45.0 m from yours, in the direction 39.0° south of east. what is the distance between karl's tent and joe's tent?

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:

explanation: look here