Question

You are camping with Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 21.0 m from yours, in the direction 23.0∘ south of east. Karl’s tent is 32.0 m from yours, in the direction 37.0∘ north of east. What is the distance between Karl’s tent and Joe’s tent?

Answer 1

Answer:

28.2 m

Explanation:

distance of Joe's tent from yours (b) = 21 m

direction of  Joe's tent from yours (p) = 23°

distance of Karl's tent from yours (c) = 32 m

direction of Karl's tent from yours (q) = 37°

distance between Joe and Karl's tent (a) = ?

from the diagram attached, we can see that the positions of the three tents form a triangle and hence we can apply the cosine rule to get the distance between Joe and Karl's tent.

let the distance between Joe and Karl's tent be = a

$a^{2} = b^{2} + c^{2} - 2bc.Cos(p+q)$

now substituting all required values into the equation above we have

$a^{2} = 21^{2} + 32^{2} - (2x21x32)x(Cos(23+37))$

$a^{2} = 793$

a = $\sqrt{793}$

a = 28.2 m