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A robot moved 10 meters towards north. It then turned 44 degrees to its right and moved another 10 meters. It then turned 55 degress to its right and moved another 10 meters. Last, it turned x degrees to its right. The robot was facing south after the last move. What is x

 Sep 8, 2019
 #1
avatar+1533 
+4

Draw a picture, you will realize that the 10 meter movements wont matter in affecting the angle and direction it is facing. So as it was assumed to be facing north in the begininng, in order for it to face south, it must turn 180.

So far it has turned 55+44 = 99 degrees. this means it needs to turn 180-99 = 81 degrees to face south.

 Sep 8, 2019
 #2
avatar+103858 
+3

See the following image :

 

 

 

Suppose the robot starts at  A  and moves 10m North to B......he then turns 44° to the right   and moves anonther 10m  to D......at D  he turns  55°  to the right and moves 10 more meters to F.....he then turns x degrees and faces due South   (along FG)

 

If we  connect BF  ....note that  angle BDF =  180 - 55   =  125°

 

Since BD  = DF....the angles DBF  and DFB  must be equal.....so  the measure of angle DFB  =  [ 180 - 125] / 2  =

 

55/2   =  27.5°

 

And angle FBG  =   90 - CBD - DBF  =  90  - 44 - 27.5  = 18.5°

 

And triangle BFG is right with angle BGF = 90°

 

So  angle  BFG  =  90 - FBG  =  90  - 18.5  =   71.5°

 

So  angles DFB  + BFG  + HFG  =  180

 

So     27.5 + 71.5 + HFG  =  180

 

99 + HFG  =  180

 

HFG =  180  - 99  =   81°  =   x  =  the number of degrees in the last turn

 

 

 

cool cool cool

 Sep 8, 2019
edited by CPhill  Sep 9, 2019
 #3
avatar+1533 
+3

Just so he isn't confused

 

So     27.5 + 71.5 + HFG  =  180

 

98 + HFG  =  180

 

98 is supposed to be 99

 

 

Good answer though! I couldn't be sure that 10 meter movements won't affect the angle, I was just using my intuition. Now you proved it!

CalculatorUser  Sep 8, 2019
edited by CalculatorUser  Sep 8, 2019
 #4
avatar+23133 
+3

A robot moved 10 meters towards north. It then turned 44 degrees to its right and moved another 10 meters.

It then turned 55 degress to its right and moved another 10 meters.

Last, it turned x degrees to its right.

The robot was facing south after the last move.

What is x

 

\(\begin{array}{|rcll|} \hline 44^\circ+55^\circ+x &=& 180^\circ \\ 99^\circ+x &=& 180^\circ \\ x &=& 180^\circ -99^\circ \\ \mathbf{x} &=& \mathbf{81^\circ} \\ \hline \end{array} \)

 

laugh

 Sep 9, 2019

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