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 23.0o south of east. Karl’s tent is 32.0 m from yours, in the direction 37.0o north of east. What is the distance between Karl’s tent and Joe’s tent?

Solution 86P Step 1 : Let us consider a graphical representation of the scenario Let us consider vectors X, K and J to represent the position vectors for you , Karl and Joe respectively Step 2 : Considering the data given Distance between you and Karl = K = 32 m 0 Angle between you and Karl = = 37 Distance between you and Joe J = 21 m 0 Angle between you and Joe = 23 Step 3 : Let us find the x and y components for Vector J It is given by J x J cos And J = J sin y Substituting the values we get J x 21 m × cos 23 0 J = 21 m × 0.9205 x J x 19.3060 i m And J y 21 m × sin 23 0 J = 21 m × 0.39073 y J y 8.2053 j m Hence we have J = 19.3060 i m 8.2053 j m Let us find the x and y components for Vector K It is given by K x K cos And K = K sin y Substituting the values we get 0 K x 32 m × cos 37 K x 32 m × 0.7986 K x 25.5563 i m 0 And K y 32 m × sin 37 K y 32 m × 0.6018 K y 19.2580 j m Hence we have K = 25.5563 i m + 19.2580 j m