You are camping with Joe andKarl.Since all three of you like your privacy,you dont pitch your tents close together.Joes tent is 21.0 m from yours, in the direct 23.0 south of east.Karls tent is 32.0 m from yours, in the direction 37.0 north of east.What is the dist between Karls tent and Joes tent?
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Draw this answer on x-axis and y-axis for better understanding.
Let your tent is at a point, we say it O (0,0), Joe's tent is at Point J (in the first quadrant) and Karl's tent is at Point K (in the fourth quadrant). So now acc. to the ques. line joining OJ will make angle of 37.0 and line joining OK will make angle of 23.0 with the x-axis.
Given, OJ = 21m. and OK = 32m.
Therefore; vector OJ = (21xcos23)i - (21xsin23)j
and vector OK = (32xcos37)i + (32xsin37)j
From vector triangle,
OJ + JK = OK => JK = OK - OJ
vector JK = (32xcos37 - 21xcos23)i + (32xsin37 + 21xsin23)j
|JK|^2 = [(32xcos37 - 21xcos23)^2 + (32xsin37 + 21xsin23)^2] m^2
Jk = 28.16m
So, the distance between Joe and Karl tent is = 28.16m or 28.20m
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