Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.49 m due east, then 0.72 m at 36o north of due east. Beetle 2 also makes two runs; the first is 1.59 m at 30o east of due north. What must be the magnitude of its second run if it is to end up at the new location of beetle 1?

Answer ; 0.86 m
Plot the routes.
From (0,0) run a line to (0.49,0) for first leg of beetle #1...run a line at 36degrees,0.72 long for second run of beetle #1...........from sine and cosine of 36 degrees, establish that final position of beetle #1 is (1.07, 0.46)
From (0,0)run a line at 30 degrees, 1.59 for first leg of beetle #2..........from sine and cosine of 30 degrees, establish that beetle #2 is at (0.8, 1.38)
Distance for beetle #2 o travel to end up with beetle # 1 (pythagoras ) = square root ( 0.27^2 + 0.82^2) = 0.86
Plot the routes.
From (0,0) run a line to (0.49,0) for first leg of beetle #1...run a line at 36degrees,0.72 long for second run of beetle #1...........from sine and cosine of 36 degrees, establish that final position of beetle #1 is (1.07, 0.46)
From (0,0)run a line at 30 degrees, 1.59 for first leg of beetle #2..........from sine and cosine of 30 degrees, establish that beetle #2 is at (0.8, 1.38)
Distance for beetle #2 o travel to end up with beetle # 1 (pythagoras ) = square root ( 0.27^2 + 0.82^2) = 0.86