Triangulation method (in e.g. photogrammetry, except this is in 2D)
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A: "A" equals left parenthesis, negative 3.3 5 , 4.7 7 , right parenthesis Has graph. To audio trace, press ALT+T.A=−3.35,4.77
2
B: "B" equals left parenthesis, 3.2 8 , 0.9 3 , right parenthesis Has graph. To audio trace, press ALT+T.B=3.28,0.93
3
Baseline: "L" Subscript, "A" "B" , Baseline equals segment left parenthesis, "A" , "B" , right parenthesis Has graph.LAB=segmentA,B
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C: "C" equals left parenthesis, 2.8 6 , 6.3 3 , right parenthesis Has graph. To audio trace, press ALT+T.C=2.86,6.33
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Hidden Label: left bracket, segment left parenthesis, "A" , "C" , right parenthesis , segment left parenthesis, "B" , "C" , right parenthesis , right bracket equals undefined Has graph.segmentA,C,segmentB,C
2 element list
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Expression 7: "P" Subscript, "L" "C" , Baseline equals perpendicular left parenthesis, "L" Subscript, "A" "B" , Baseline , "C" , right parenthesis Has graph.PLC=perpendicularLAB,C
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Expression 8: "P" Subscript, "A" , Baseline equals parallel left parenthesis, "P" Subscript, "L" "C" , Baseline , "A" , right parenthesis Has graph.PA=parallelPLC,A
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Expression 9: "P" Subscript, "B" , Baseline equals parallel left parenthesis, "P" Subscript, "L" "C" , Baseline , "B" , right parenthesis Has graph.PB=parallelPLC,B
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Hidden Label: "P" Subscript, "L" "P" , Baseline equals intersection left parenthesis, "L" Subscript, "A" "B" , Baseline , "P" Subscript, "L" "C" , Baseline , right parenthesis equals left parenthesis, 0.6 2 3 5 2 7 4 8 1 7 9 4 , 2.4 6 8 5 9 0 4 1 7 7 8 , right parenthesis Has graph. To audio trace, press ALT+T.PLP=intersectionLAB,PLC
Label: "A" Subscript, "A" , Baseline equals angle left parenthesis, "P" Subscript, "L" "P" , Baseline , "A" , "C" , right parenthesis Has graph.AA=anglePLP,A,C
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Label: "A" Subscript, "B" , Baseline equals angle left parenthesis, "P" Subscript, "L" "P" , Baseline , "B" , "C" , right parenthesis Has graph.AB=anglePLP,B,C
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Label: "L" Subscript, "P" "C" , Baseline equals segment left parenthesis, "P" Subscript, "L" "P" , Baseline , "C" , right parenthesis Has graph.LPC=segmentPLP,C
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Hidden Label: "M" Subscript, "P" , Baseline equals midpoint left parenthesis, "L" Subscript, "A" "B" , Baseline , right parenthesis equals left parenthesis, negative 0.0 3 5 , 2.8 5 , right parenthesis Has graph. To audio trace, press ALT+T.MP=midpointLAB
equals=
left parenthesis, negative 0.0 3 5 , 2.8 5 , right parenthesis−0.035,2.85
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Expression 15: "F" Subscript, "U" , Baseline equals left parenthesis, "x" minus "A" . "x" , right parenthesis left parenthesis, "A" . "y" minus "B" . "y" , right parenthesis plus left parenthesis, "y" minus "A" . "y" , right parenthesis left parenthesis, "B" . "x" minus "A" . "x" , right parenthesisFU=x−A.xA.y−B.y+y−A.yB.x−A.x
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Expression 16: "F" Subscript, "A" , Baseline equals left parenthesis, "x" minus "A" . "x" , right parenthesis left parenthesis, "B" . "x" minus "A" . "x" , right parenthesis plus left parenthesis, "y" minus "A" . "y" , right parenthesis left parenthesis, "B" . "y" minus "A" . "y" , right parenthesisFA=x−A.xB.x−A.x+y−A.yB.y−A.y
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Expression 17: "F" Subscript, "B" , Baseline equals left parenthesis, "x" minus "B" . "x" , right parenthesis left parenthesis, "A" . "x" minus "B" . "x" , right parenthesis plus left parenthesis, "y" minus "B" . "y" , right parenthesis left parenthesis, "A" . "y" minus "B" . "y" , right parenthesisFB=x−B.xA.x−B.x+y−B.yA.y−B.y
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Expression 18: min left parenthesis, "F" Subscript, "U" , Baseline , "F" Subscript, "A" , Baseline , "F" Subscript, "B" , Baseline , right parenthesis greater than or equal to 0 Has graph.minFU,FA,FB≥0
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Expression 19: theta Subscript, "A" , Baseline equals arc tangent left parenthesis, "C" . "y" minus "A" . "y" , "C" . "x" minus "A" . "x" , right parenthesis equals 14.1 0 1 3 5 2 2 8 0 3θA=arctanC.y−A.y,C.x−A.x
equals=
14.1 0 1 3 5 2 2 8 0 314.1013522803
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Expression 20: theta Subscript, "B" , Baseline equals arc tangent left parenthesis, "C" . "y" minus "B" . "y" , "C" . "x" minus "B" . "x" , right parenthesis equals 94.4 4 7 3 8 4 8 5 0 1θB=arctanC.y−B.y,C.x−B.x
equals=
94.4 4 7 3 8 4 8 5 0 194.4473848501
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Expression 21: "D" Subscript, "A" "B" , Baseline equals StartRoot, left parenthesis, "B" . "x" minus "A" . "x" , right parenthesis squared plus left parenthesis, "B" . "y" minus "A" . "y" , right parenthesis squared , EndRoot equals 7.6 6 1 7 5 5 6 7 3 4 7DAB=B.x−A.x2+B.y−A.y2
equals=
7.6 6 1 7 5 5 6 7 3 4 77.66175567347
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Expression 22: "A" . "y" plus left parenthesis, "x" minus "A" . "x" , right parenthesis StartFraction, "B" . "y" minus "A" . "y" Over "B" . "x" minus "A" . "x" , EndFractionA.y+x−A.xB.y−A.yB.x−A.x
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(dividing by zero ain't good)
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Expression 24: left parenthesis, "B" . "y" minus "A" . "y" , right parenthesis "x" minus left parenthesis, "B" . "x" minus "A" . "x" , right parenthesis "y" plus "A" . "y" left parenthesis, "B" . "x" minus "A" . "x" , right parenthesis minus "A" . "x" left parenthesis, "B" . "y" minus "A" . "y" , right parenthesis equals 0B.y−A.yx−B.x−A.xy+A.yB.x−A.x−A.xB.y−A.y=0
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Expression 25: phi equals arc tangent left parenthesis, "B" . "y" minus "A" . "y" , "B" . "x" minus "A" . "x" , right parenthesis equals negative 30.0 7 8 8 0 1 4 3 7 7ϕ=arctanB.y−A.y,B.x−A.x
equals=
negative 30.0 7 8 8 0 1 4 3 7 7−30.0788014377
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Expression 26: "D" Subscript, "A" "B" , Baseline times StartFraction, sin left parenthesis, theta Subscript, "A" , Baseline minus phi , right parenthesis sin left parenthesis, theta Subscript, "B" , Baseline minus phi , right parenthesis Over sin left parenthesis, theta Subscript, "B" , Baseline minus theta Subscript, "A" , Baseline , right parenthesis , EndFraction equals 4.4 6 2 3 1 9 2 7 2 1 2DAB·sinθA−ϕsinθB−ϕsinθB−θA
