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 26.5 from yours, in the direction 21.0 north of east. Karl's tent is 28.5 from yours, in the direction 40.5 south of east.
To find the distance between Joe's tent and Karl's tent, you can use the concept of relative displacement.
First, we need to find the components of the displacement in the north and east directions for each tent.
For Joe's tent:
North component = 26.5 sin(21.0°)
East component = 26.5 cos(21.0°)
For Karl's tent:
North component = 28.5 sin(40.5°)
East component = 28.5 cos(40.5°)
Next, we can calculate the displacement between Joe's and Karl's tents by subtracting the corresponding components:
North displacement = Joe's North component - Karl's North component
East displacement = Joe's East component - Karl's East component
Finally, we can use the Pythagorean theorem to find the distance between Joe's and Karl's tents:
Distance = √(North displacement^2 + East displacement^2)