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

Saketh Sep 8, 2019

#1**+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.

CalculatorUser Sep 8, 2019

#2**+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

CPhill Sep 8, 2019

#3**+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

#4**+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**

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

heureka Sep 9, 2019