Let A=(0,0), B=(7,2), C=(3,4), D=(3,7) and E=(-1,5). Cameron walks the polygonal path ABCDEA, writing down the number of degrees turned at each corner. What is the sum of these five numbers? Notice that ABCDE in not a convex pentagon.
I got 491.(using a protractor) Could someone take a look at my attached work?
oops, on my last line of attached work i meant if angle c was convex
March 10th 2011, 04:00 PM
Why does convexity make any difference? Don't you have to end up where you started and facing the direction you started?
March 11th 2011, 10:36 AM
Hi Veronica 1999,
I calculated the angle of the first turn at B to be 137.5. At C 116.6and 116.6 at D.Finish and let me know if you get the right answer
March 11th 2011, 10:45 AM
TKHunny is suggesting a more theoretical approach, with which I agree. Are we explicitly calculating each angle as a means of verification?
March 11th 2011, 01:08 PM
While sketching, I found the problem more complex than anticipated.
| Y *
| . β *
| . *
| o X
| C * .
| * α .
| * B
A o - - - - - - - - - - - - -
When he walks from to , he is walking in the direction
To walk to , he turns through . . . not
Then he walks from to , in the direction
To walk to , he turns through
And so on . . .
March 11th 2011, 04:15 PM
I had the right idea but made a mistake in the turn at C I recalculated all the turns with the following results 137,5,63.5,116.5,74.5, 85.35.Is this correct?