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 19.5 from yours, in the direction 21.5 north of east. Karl's tent is 41.0 from yours, in the direction 41.0 south of east.

Question

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

Answer 1

The three tents form a triangle with side lengths a = 19.5, b = 41.0, and included angle between them of 62.5 degrees. You want the length of the thrid side, c.

The angle between the directions to the two tents, as seen from "my" tent, is 62.5 degrees. For the distance between them (c), use the law of cosines

c^2 = a^2 + b^2 - 2 a b cos62.5
= 19.5^2 + 41^2 - 2*19.5*41*(0.4617)
= 1323.0
c = 36.37 m

Answer 2

thanks you so much