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The New Coffee Room

  1. TNCR
  2. General Discussion
  3. Puzzle time - Find the angle

Puzzle time - Find the angle

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  • AxtremusA Away
    AxtremusA Away
    Axtremus
    wrote on last edited by
    #2

    Found it!
    alt text

    1 Reply Last reply
    • Doctor PhibesD Offline
      Doctor PhibesD Offline
      Doctor Phibes
      wrote on last edited by Doctor Phibes
      #3

      That's about 115 degrees.

      I was only joking

      1 Reply Last reply
      • KlausK Offline
        KlausK Offline
        Klaus
        wrote on last edited by Klaus
        #4

        The problem looks underspecified. You'd need to give us some other angles or lengths or areas or whatnot. Are the top left and top right angles 90 degrees? Are the shaded triangles supposed to have the same angles? Are the side length of the shaded triangles all the same, respectively?

        taiwan_girlT 1 Reply Last reply
        • KlausK Klaus

          The problem looks underspecified. You'd need to give us some other angles or lengths or areas or whatnot. Are the top left and top right angles 90 degrees? Are the shaded triangles supposed to have the same angles? Are the side length of the shaded triangles all the same, respectively?

          taiwan_girlT Offline
          taiwan_girlT Offline
          taiwan_girl
          wrote on last edited by
          #5

          @Klaus said in Puzzle time - Find the angle:

          The problem looks underspecified. You'd need to give us some other angles or lengths or areas or whatnot. Are the top left and top right angles 90 degrees? Are the shaded triangles supposed to have the same angles? Are the side length of the shaded triangles all the same, respectively?

          I agree. Without the little "square" to indicate a 90 degree angle and other numbers, it is impossible to solve (at least I think so!!! LOL)

          1 Reply Last reply
          • KlausK Offline
            KlausK Offline
            Klaus
            wrote on last edited by
            #6

            119 degrees.

            Here's my reasoning.

            ||
            b275088f-c78d-431f-bf86-a798a1cffc16-image.png
            ||

            taiwan_girlT 1 Reply Last reply
            • KlausK Klaus

              119 degrees.

              Here's my reasoning.

              ||
              b275088f-c78d-431f-bf86-a798a1cffc16-image.png
              ||

              taiwan_girlT Offline
              taiwan_girlT Offline
              taiwan_girl
              wrote on last edited by
              #7

              @Klaus said in Puzzle time - Find the angle:

              119 degrees.

              Here's my reasoning.

              ||
              b275088f-c78d-431f-bf86-a798a1cffc16-image.png
              ||

              LOL

              1 Reply Last reply
              • jon-nycJ Online
                jon-nycJ Online
                jon-nyc
                wrote on last edited by
                #8

                Sorry - the two shaded triangles are equilateral.

                "You never know what worse luck your bad luck has saved you from."
                -Cormac McCarthy

                KlausK 1 Reply Last reply
                • jon-nycJ jon-nyc

                  Sorry - the two shaded triangles are equilateral.

                  KlausK Offline
                  KlausK Offline
                  Klaus
                  wrote on last edited by Klaus
                  #9

                  @jon-nyc said in Puzzle time - Find the angle:

                  Sorry - the two shaded triangles are equilateral.

                  But that alone is not enough. For instance, I could shrink one of the triangles by 50% and change the angle. You'd need something else like "the area of the bigger one is twice the area of the smaller".

                  1 Reply Last reply
                  • George KG Offline
                    George KG Offline
                    George K
                    wrote on last edited by
                    #10

                    I think I hated trig even more than I hated statistics.

                    "Now look here, you Baltic gas passer... " - Mik, 6/14/08

                    The saying, "Lite is just one damn thing after another," is a gross understatement. The damn things overlap.

                    1 Reply Last reply
                    • KlausK Offline
                      KlausK Offline
                      Klaus
                      wrote on last edited by
                      #11

                      How about statistical trigonometry?

                      George KG 1 Reply Last reply
                      • KlausK Klaus

                        How about statistical trigonometry?

                        George KG Offline
                        George KG Offline
                        George K
                        wrote on last edited by
                        #12

                        @Klaus said in Puzzle time - Find the angle:

                        How about statistical trigonometry?

                        alt text

                        "Now look here, you Baltic gas passer... " - Mik, 6/14/08

                        The saying, "Lite is just one damn thing after another," is a gross understatement. The damn things overlap.

                        1 Reply Last reply
                        • jon-nycJ Online
                          jon-nycJ Online
                          jon-nyc
                          wrote on last edited by
                          #13

                          Definitely there is a solution

                          "You never know what worse luck your bad luck has saved you from."
                          -Cormac McCarthy

                          1 Reply Last reply
                          • jon-nycJ Online
                            jon-nycJ Online
                            jon-nyc
                            wrote on last edited by
                            #14

                            No cheating and saying ‘since it’s true for any relative size triangles let me assume they’re the same size and figure out that special case’.

                            "You never know what worse luck your bad luck has saved you from."
                            -Cormac McCarthy

                            1 Reply Last reply
                            • KlausK Offline
                              KlausK Offline
                              Klaus
                              wrote on last edited by
                              #15

                              Oh, I see. The relative size doesn't matter. It's always 120 degrees.

                              b726227f-605b-4357-b268-fda0505616fa-image.png

                              1 Reply Last reply
                              • jon-nycJ Online
                                jon-nycJ Online
                                jon-nyc
                                wrote on last edited by
                                #16

                                Can you prove it?

                                "You never know what worse luck your bad luck has saved you from."
                                -Cormac McCarthy

                                1 Reply Last reply
                                • KlausK Offline
                                  KlausK Offline
                                  Klaus
                                  wrote on last edited by Klaus
                                  #17

                                  Well, I assume if I set up a formula for the angle given side length a and b for the triangles, then simplify using textbook identities for trigonometric functions, the a's and b's will magically cancel each other all out and I'll just get the 120 degrees.

                                  There should be a tool online that turns geometric constructions into algebraic equations. There's pizza in the oven, so I can't be bothered to do that by hand right now 🙂

                                  1 Reply Last reply
                                  • Doctor PhibesD Offline
                                    Doctor PhibesD Offline
                                    Doctor Phibes
                                    wrote on last edited by
                                    #18

                                    I'm going with 120 degrees.

                                    My reasoning is that Klaus knows about this stuff.

                                    I was only joking

                                    1 Reply Last reply
                                    • Doctor PhibesD Offline
                                      Doctor PhibesD Offline
                                      Doctor Phibes
                                      wrote on last edited by
                                      #19

                                      Sorry, I should probably have put that in a spoiler

                                      I was only joking

                                      1 Reply Last reply
                                      • jon-nycJ Online
                                        jon-nycJ Online
                                        jon-nyc
                                        wrote on last edited by
                                        #20

                                        You can do it without complex trig identities. In your head in fact.

                                        "You never know what worse luck your bad luck has saved you from."
                                        -Cormac McCarthy

                                        1 Reply Last reply
                                        • KlausK Offline
                                          KlausK Offline
                                          Klaus
                                          wrote on last edited by
                                          #21

                                          c972b347-db4e-4716-92d7-539ef349e549-image.png

                                          The sum of angles in the upper quadrilateral is 360 degrees. The top one must be 60 degrees. Beta and Gamma add up to 180 degrees. That leaves the desired 120 degrees. The only missing step is why beta and gamma add up to 180.

                                          Something like that?

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