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

Answer:

46 meters

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:

$a^2 = 15^2 m^2 + 42^2 m^2 - 2 \times 15 \times 42 \times cos(64.5)$

$a = \sqrt{2111.46 m^2}$

$a = 46 m$