MY 11 TRISECTION APPROXIMATION METHODS Pg. 118
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FIG. 27
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1.
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Draw any suitable straight line AOB with line AO = 2 units and
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from pt O draw a straight line OC = 1 unit with ÐCOB = 3Æ,
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as shown in FIG. 27 above.
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2.
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Join pt A & C with a straight line.
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Let ÐCAB = b.
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3.
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Draw line CD so that ÐDCO = 2Æ and meets line ADOB at pt D.
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4.
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Since ÐCOB = 3Æ is the exterior angle of DCDO.
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| Pg. 119
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Then ÐCDO = ÐCOB - ÐDCO = 3Æ - 2Æ = Æ.
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Therefore ÐCDO = Æ trisects ÐCOB = 3Æ as required.
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1/sinÆ = (2-2a)/sin2Æ
[ from COSINE LAW]
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sin2Æ = 2sinÆ/cosÆ
[ from CRC TABLES]
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2 - 2a = 2cosÆ
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a = 1 - cosÆ
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2a = 2(1 - cosÆ)
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TABLE OF DEGREES vs 2a INCHES
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Æ
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3Æ
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2a"
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| 1° | 3° | 0.000305''
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| 2° | 6° | 0.001218''
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| 3° | 9° | 0.002741''
| | Pg. 120
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| 4° | 12° | 0.004872''
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| 5° | 15° | 0.007611''
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| 6° | 18° | 0.010956''
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| 7° | 21° | 0.014908''
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| 7° 9' 59" | 0.015625'' | 1/64"
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| 8° | 24° | 0.019464''
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| 9° | 27° | 0.024623''
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| 10° | 30° | 0.030384''
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| 10° 8' 30" | 0.03125'' | 1/32"
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| 11° | 33° | 0.036746''
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| 12° | 36° | 0.043705''
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| 12° 25' 45" | 0.046875'' | 3/64"
| | Pg. 121
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| 13° | 39° | 0.051260''
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| 14° | 42° | 0.059409''
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| 14° 21' 41" | 0.0625'' | 1/16"
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| 15° | 45° | 0.068148''
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| 16° | 48° | 0.077477''
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| 16° 4' 2" | 0.078125'' | 5/64"
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| 17° | 51° | 0.087390''
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| 17° 36' 44" | 0.09375'' | 3/32"
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| 18° | 54° | 0.097887''
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| 19° | 57° | 0.108963''
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| 19° 2' 10" | 0.109375'' | 7/64"
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| 20° | 60° | 0.120615''
| | Pg. 122
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| 20° 21' 50" | 0.125'' | 1/8"
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| 21° | 63° | 0.132839''
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| 21° 36' 49" | 0.140625'' | 9/64"
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| 22° | 66° | 0.145632''
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| 22° 47' 53" | 0.15625'' | 5/32"
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| 23° | 69° | 0.158990''
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| 23° 55' 37" | 0.171875'' | 11/64"
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| 24° | 72° | 0.172909''
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| 25° | 75° | 0.187384''
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| 25° 0' 28" | 0.1875'' | 3/16"
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| 26° | 78° | 0.202412''
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| 26° 2' 47" | 0.203125'' | 13/64"
| | Pg. 123
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| 27° | 81° | 0.217987''
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| 27° 2' 53" | 0.21875'' | 7/32"
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| 28° | 84° | 0.234105''
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| 28° 0' 59" | 0.234375'' | 15/64"
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| 28° 57' 18" | 0.25'' | 1/4"
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| 29° | 87° | 0.250761''
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| 29° 51' 59" | 0.265625'' | 17/64"
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| 30° | 90° | 0.267949''
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| 30° 45' 12" | 0.28125'' | 9/32"
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| 31° | 93° | 0.285665''
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| 31° 37'4" | 0.296875'' | 19/64"
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| 32° | 96° | 0.303904''
| | Pg. 124
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| 32° 27' 42" | 0.3125'' | 5/16"
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| 33° | 99° | 0.622659''
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| 33° 17' 11" | 0.328125'' | 21/64"
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| 34° | 102° | 0.341925''
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| 34° 5' 36" | 0.34375'' | 11/32"
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| 34° 53' 2" | 0.359375'' | 23/74"
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| 35° | 105° | 0.361696''
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| 35° 39' 32" | 0.375'' | 3/8"
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| 36° | 108° | 0.381966''
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| 36° 25' 11" | 0.390625'' | 25/64"
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| 37° | 111° | 0.402729''
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| 37° 10' 2" | 0.40625'' | 13/32"
| | Pg. 125
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| 37° 54' 7" | 0.421875'' | 27/64"
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| 38° | 114° | 0.423978''
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| 38° 37' 29" | 0.4375'' | 7/16"
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| 39° | 117° | 0.445708''
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| 39° 20' 11" | 0.453125'' | 29/64"
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| 40° | 120° | 0.467911''
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| 40° 2' 14" | 0.46875'' | 15/32"
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| 40° 43' 41" | 0.484375'' | 31/64"
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| 41° | 123° | 0.490581''
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| 41° 24' 34" | 0.5'' | 1/2"
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| 42° | 126° | 0.513710''
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| 42° 44' 44" | 0.53125'' | 17/32"
| | Pg. 126
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| 42° 33' 54" | 0.515625'' | 33/64"
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| 43° | 129° | 0.537293''
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| 43° 24' 3" | 0.546875'' | 35/64"
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| 44° | 132° | 0.561320''
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| 44° 2' 55" | 0.5625'' | 9/16"
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| 44° 41' 19" | 0.578125'' | 37/64"
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| 45° | 135° | 0.585786''
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| 45° 19' 18" | 0.59375'' | 19/32"
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| 45° 56' 52" | 0.609375'' | 39/64"
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| 46° | 138° | 0.618683''
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