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{"sheet":"Area Triángulo 1","index":0,"n_rows":23,"n_cols":15,"rows_kept":23,"cut":false,"hidden":false,"merged":[[21,11,22,11],[1,5,1,10],[1,11,1,14],[6,0,7,2],[7,5,7,10],[7,11,7,12]]}
[]
["Coordenadas Tríangulo",null,null,null,null,"1. Matriz con Excel ↓",null,null,null,null,null,"2. Matemáticamente ↓"]
[null,null,null,null,null,"Matriz Determinada →",null,null,"MDETERM",null,null,{"$f":"A2","v":"Coordenadas Tríangulo"}]
["A",2,9,"→",{"$f":"A4&\" (\"&B4&\" , \"&C4&\")\"","v":"A (2 , 9)"},null,1,{"$f":"B4","v":2},9,null,null,{"$f":"H4","v":2},9]
["B",-2,1,"→",{"$f":"A5&\" (\"&B5&\" , \"&C5&\")\"","v":"B (-2 , 1)"},"A=",1,-2,1,null,null,-2,1]
["C",-5,3,"→",{"$f":"A6&\" (\"&B6&\" , \"&C6&\")\"","v":"C (-5 , 3)"},null,1,-5,3,"Area",{"$f":"1/2*ABS(MDETERM(G4:I6))","v":16},-5,3,"Area ",{"$f":"ABS(L4*M5+L5*M6+L6*M7-L7*M6-L6*M5-L5*M4)/2","v":16}]
["Coordenadas a cambiar ↑",null,null,null,null,null,null,null,null,null,null,{"$f":"L4","v":2},{"$f":"M4","v":9}]
[null,null,null,null,null,"3. Con Razones Trigonométricas",null,null,null,null,null,"4. Con Fórmula de \"Herón\"",null,"Posición"]
[null,null,null,null,null,null,null,null,null,null,null,"Distancia 1",{"$f":"((L4-L5)^2+(M4-M5)^2)^(1/2)","v":8.9442719099991592},{"$f":"_xlfn.RANK.EQ(M9,$M$9:$M$11,0)+ COUNTIF($M$9:M9,M9)-1","v":2}]
[null,null,null,null,null,null,null,null,null,null,null,"Distancia 2",{"$f":"((L5-L6)^2+(M5-M6)^2)^(1/2)","v":3.6055512754639891},{"$f":"_xlfn.RANK.EQ(M10,$M$9:$M$11,0)+ COUNTIF($M$9:M10,M10)-1","v":3}]
[null,null,null,null,null,null,null,null,null,null,null,"Distancia 3",{"$f":"((L6-L7)^2+(M6-M7)^2)^(1/2)","v":9.2195444572928871},{"$f":"_xlfn.RANK.EQ(M11,$M$9:$M$11,0)+ COUNTIF($M$9:M11,M11)-1","v":1}]
[null,null,null,null,null,null,null,null,null,"Area=",{"$f":"1/2*(INDEX($M$9:$N$11,MATCH(2,$N$9:$N$11,0),1)*MAX($M$9:$M$11))*SIN((MIN($J$17:$J$19)*PI()/180))","v":16},"p=",{"$f":"SUM(M9:M11)/2","v":10.884683821378019},"Area=",{"$f":"($M$12*($M$12-$M$9)*($M$12-$M$10)*($M$12-$M$11))^(1/2)","v":16.000000000000011}]
[]
[]
[]
["No Eliminar esta Fila→",null,null,null,null,{"$f":"J6&\"= \"&K6","v":"Area= 16"}]
[null,null,null,null,null,null,"Cos C",{"$f":"($M$10^2+$M$11^2-$M$9^2)/(2*$M$10*$M$11)","v":0.27074557691828388},"Ángulo C=",{"$f":"ACOS(H17)*180/PI()","v":74.291362170984272}]
[null,null,null,null,null,null,"Cos B",{"$f":"($M$9^2+$M$10^2-$M$11^2)/(2*$M$9*$M$10)","v":0.12403473458920869},"Ángulo B=",{"$f":"ACOS(H18)*180/PI()","v":82.874983651098177}]
[null,null,null,null,null,null,"Cos A",{"$f":"($M$9^2+$M$11^2-$M$10^2)/(2*$M$9*$M$11)","v":0.92163537513806526},"Ángulo A=",{"$f":"ACOS(H19)*180/PI()","v":22.833654177917545}]
[null,null,null,null,null,null,null,null,"Σ=",{"$f":"SUM(J17:J19)","v":180},"Hipotemusa² =",null,{"$f":"CONCATENATE(\"a\",\"²\",\" + \",\"b\",\"²\")","v":"a² + b²"}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"MAX($M$9:$M$11)^2","v":85},"=",{"$f":"(INDEX(M9:N11,MATCH(2,$N$9:$N$11,0),1))^2+MIN($M$9:$M$11)^2","v":93.000000000000014},{"$f":"IF(MAX(M9:M11)^2=(MIN(M9:M11)^2+M11^2),\"Es Tríangulo Rectángulo\", \"No es Triángulo Rectángulo\")","v":"No es Triángulo Rectángulo"}]
[null,null,null,null,null,null,null,null,null,null,null,"Alturas","h1=",{"$f":"(2/MIN($M$9:$M$11)*($M$12*($M$12-$M$9)*($M$12-$M$10)*($M$12-$M$11))^(1/2))","v":8.8752031396036717}]
[null,null,null,null,null,null,null,null,null,null,null,null,"h2=",{"$f":"(2/M11)*($M$12*($M$12-$M$9)*($M$12-$M$10)*($M$12-$M$11))^(1/2)","v":3.4708873250985008}]

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[]
["Coordenadas Tríangulo",null,null,null,null,"1. Matriz con Excel ↓",null,null,null,null,null,"2. Matemáticamente ↓"]
[null,null,null,null,null,"Matriz Determinada →",null,null,"MDETERM",null,null,{"$f":"A2","v":"Coordenadas Tríangulo"}]
["A",-5,2,"→",{"$f":"A4&\" (\"&B4&\" , \"&C4&\")\"","v":"A (-5 , 2)"},null,1,{"$f":"B4","v":-5},2,null,null,{"$f":"H4","v":-5},2]
["B",-5,8,"→",{"$f":"A5&\" (\"&B5&\" , \"&C5&\")\"","v":"B (-5 , 8)"},"A=",1,-5,8,null,null,-5,8]
["C",9,2,"→",{"$f":"A6&\" (\"&B6&\" , \"&C6&\")\"","v":"C (9 , 2)"},null,1,9,2,"Area",{"$f":"1/2*ABS(MDETERM(G4:I6))","v":42},9,2,"Area ",{"$f":"ABS(L4*M5+L5*M6+L6*M7-L7*M6-L6*M5-L5*M4)/2","v":42}]
["Coordenadas a cambiar ↑",null,null,null,null,null,null,null,null,null,null,{"$f":"L4","v":-5},{"$f":"M4","v":2}]
[null,null,null,null,null,"3. Con Razones Trigonométricas",null,null,null,null,null,"4. Con Fórmula de \"Herón\"",null,"Posición"]
[null,null,null,null,null,null,null,null,null,null,null,"Distancia 1",{"$f":"((L4-L5)^2+(M4-M5)^2)^(1/2)","v":6},{"$f":"_xlfn.RANK.EQ(M9,$M$9:$M$11,0)+ COUNTIF($M$9:M9,M9)-1","v":3}]
[null,null,null,null,null,null,null,null,null,null,null,"Distancia 2",{"$f":"((L5-L6)^2+(M5-M6)^2)^(1/2)","v":15.231546211727817},{"$f":"_xlfn.RANK.EQ(M10,$M$9:$M$11,0)+ COUNTIF($M$9:M10,M10)-1","v":1}]
[null,null,null,null,null,null,null,null,null,null,null,"Distancia 3",{"$f":"((L6-L7)^2+(M6-M7)^2)^(1/2)","v":14},{"$f":"_xlfn.RANK.EQ(M11,$M$9:$M$11,0)+ COUNTIF($M$9:M11,M11)-1","v":2}]
[null,null,null,null,null,null,null,null,null,"Area=",{"$f":"1/2*(INDEX($M$9:$N$11,MATCH(2,$N$9:$N$11,0),1)*MAX($M$9:$M$11))*SIN((MIN($J$17:$J$19)*PI()/180))","v":42.000000000000028},"p=",{"$f":"SUM(M9:M11)/2","v":17.615773105863909},"Area=",{"$f":"($M$12*($M$12-$M$9)*($M$12-$M$10)*($M$12-$M$11))^(1/2)","v":42}]
[]
[]
[]
["No Eliminar esta Fila→",null,null,null,null,{"$f":"J6&\"= \"&K6","v":"Area= 42"}]
[null,null,null,null,null,null,"Cos C",{"$f":"($M$10^2+$M$11^2-$M$9^2)/(2*$M$10*$M$11)","v":0.91914503001805781},"Ángulo C=",{"$f":"ACOS(H17)*180/PI()","v":23.198590513648202}]
[null,null,null,null,null,null,"Cos B",{"$f":"($M$9^2+$M$10^2-$M$11^2)/(2*$M$9*$M$10)","v":0.39391929857916763},"Ángulo B=",{"$f":"ACOS(H18)*180/PI()","v":66.801409486351815}]
[null,null,null,null,null,null,"Cos A",{"$f":"($M$9^2+$M$11^2-$M$10^2)/(2*$M$9*$M$11)","v":-1.6917684184764289E-16},"Ángulo A=",{"$f":"ACOS(H19)*180/PI()","v":90.000000000000014}]
[null,null,null,null,null,null,null,null,"Σ=",{"$f":"SUM(J17:J19)","v":180.00000000000003},"Hipotemusa² =",null,{"$f":"CONCATENATE(\"a\",\"²\",\" + \",\"b\",\"²\")","v":"a² + b²"}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"MAX($M$9:$M$11)^2","v":232.00000000000003},"=",{"$f":"(INDEX(M9:N11,MATCH(2,$N$9:$N$11,0),1))^2+MIN($M$9:$M$11)^2","v":232},{"$f":"IF(MAX(M9:M11)^2=(MIN(M9:M11)^2+M11^2),\"Es Tríangulo Rectángulo\", \"No es Triángulo Rectángulo\")","v":"Es Tríangulo Rectángulo"}]
[null,null,null,null,null,null,null,null,null,null,null,"Alturas","h1=",{"$f":"(2/MIN($M$9:$M$11)*($M$12*($M$12-$M$9)*($M$12-$M$10)*($M$12-$M$11))^(1/2))","v":14}]
[null,null,null,null,null,null,null,null,null,null,null,null,"h2=",{"$f":"(2/M11)*($M$12*($M$12-$M$9)*($M$12-$M$10)*($M$12-$M$11))^(1/2)","v":6}]