Question

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 15.0 m from yours, in the direction 22.5^\circ north of east. Karl's tent is 42.0 m from yours, in the direction 34.0^\circ south of east

What is the distance between Karl's tent and Joe's tent?

Answer 1

46 meters

Step-by-step explanation:

In the figure you can see law of cosines.

In your case

α = 22.5° + 42 ° = 64.5 °

b = 15 m (distance between your's tent and Joe's tent)

c = 42 m (distance between your's tent and Karl's tent)

a is the distance between Joe's tent and Karl's tent

Replacing in the first equation:

`a^2 = 15^2 m^2 + 42^2 m^2 - 2 * 15 * 42 * cos(64.5)`

`a = √(2111.46 m^2)`

`a = 46 m`