{"text_format":"1","workbook":"xlsx","n_sheets":8,"sheets":["INICIO","DISTANCIA  2 PUNTOS INACCESIBLE","DISTANCIA  2 PUNTOS 1 INACCESIB","ALTURA DE PIE ACCESIBLE","ALTURA DE PIE INACCESIBLE I","ALTURA DE PIE INACCESIBLE II","ALTURA DE PIE INACCESIBLE (2)","ALTURA DE PIE INACCESIBLE (3)"],"not_rendered":{"charts":0,"images":34,"macros":1,"external_links":0,"defined_names":7,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"INICIO","index":0,"n_rows":9,"n_cols":3,"rows_kept":9,"cut":false,"hidden":false,"merged":[[1,2,2,7],[4,2,4,7],[6,2,6,7]]}
[]
[null,null,"CALCULO DE DISTANCIAS Y ALTURAS"]
[]
[]
[null,null,"Realizado por Manuel Justicia Pardo. "]
[]
[null,null,"Abril de 2016"]
[]
[null,null,"Selecciona el tipo de problema que tienes que solucionar:"]

{"sheet":"DISTANCIA  2 PUNTOS INACCESIBLE","index":1,"n_rows":32,"n_cols":17,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"DISTANCIA ENTRE DOS PUNTOS INACCESIBLES:"]
[]
[]
[null,null,null,null,null,null,"Medidas que tenemos que tomar:"]
[]
[null,null,null,null,null,null,"Distancia entre los dos puntos de observación A y B: "]
[]
[null,null,null,null,null,null,null,null,"GRADOS CENTESIMALES",null,null,"GRADOS SEXAGESIMALES",null,null,null,null,"RADIANES"]
[]
[null,null,null,null,null,null,"Ángulo α",null,null,null,null,null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"Mide\",\"\"),IF(L12=\"\",\"\",IF(L12*100/90=I12,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"mide\",L12*PI()/180),I12*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo β",null,null,null,null,null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"Mide\",\"\"),IF(L14=\"\",\"\",IF(L14*100/90=I14,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"mide\",L14*PI()/180),I14*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo γ",null,null,null,null,null,null,{"$f":"IF(I16=\"\",IF(L16=\"\",\"Mide\",\"\"),IF(L16=\"\",\"\",IF(L16*100/90=I16,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I16=\"\",IF(L16=\"\",\"mide\",L16*PI()/180),I16*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo δ",null,null,null,null,null,null,{"$f":"IF(I18=\"\",IF(L18=\"\",\"Mide\",\"\"),IF(L18=\"\",\"\",IF(L18*100/90=I18,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I18=\"\",IF(L18=\"\",\"mide\",L18*PI()/180),I18*PI()/200)","v":"mide"}]
[]
[]
[null,"La distancia entre A y B es conocida y también lo son los ángulos α y β. Teniendo en cuenta esto puedo reslolver el triángulo ADB. Y obtengo la distancia entre A y D."]
[null,"Por otro lado conozco la distancia entre A y B y los ángulos β y γ. De manera que puedo resolver el triángulo ACB. Y ya tengo la distancia entre A y C."]
[null,"Por último resolvemos el triángulo ACD, del que conocemos dos lados y un ángulo."]
[]
[null,"La distancia desde el observador A al punto D es:",null,null,null,{"$f":"IF(L8=\"\",\"Tienes primero que medir la distancia entre los dos puntos de observación\",L8*SIN(Q18)/SIN(PI()-Q12-21))","v":"Tienes primero que medir la distancia entre los dos puntos de observación"}]
[]
[]
[null,"La distancia desde el observador A al punto C es:",null,null,null,{"$f":"IF(L8=\"\",\"Tienes primero que medir la distancia entre los dos puntos de observación\",L8*SIN(Q14)/SIN(PI()-Q14-Q16))","v":"Tienes primero que medir la distancia entre los dos puntos de observación"}]
[]
[]
[]
[null,"La distancia entre los dos puntos inaccesibles es:",null,null,null,{"$f":" SQRT(F25^2+F28^2-2*F25*F28*COS(Q16-Q12))","v":{"$error":"#VALUE!"}}]

{"sheet":"DISTANCIA  2 PUNTOS 1 INACCESIB","index":2,"n_rows":32,"n_cols":17,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"DISTANCIA ENTRE DOS PUNTOS INACCESIBLES:"]
[]
[]
[null,null,null,null,null,null,"Medidas que tenemos que tomar:"]
[]
[null,null,null,null,null,null,"Distancia entre los dos puntos de observación A y B: "]
[]
[null,null,null,null,null,null,null,null,"GRADOS CENTESIMALES",null,null,"GRADOS SEXAGESIMALES",null,null,null,null,"RADIANES"]
[]
[null,null,null,null,null,null,"Ángulo α",null,null,null,null,null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"Mide\",\"\"),IF(L12=\"\",\"\",IF(L12*100/90=I12,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"mide\",L12*PI()/180),I12*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo β",null,null,null,null,null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"Mide\",\"\"),IF(L14=\"\",\"\",IF(L14*100/90=I14,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"mide\",L14*PI()/180),I14*PI()/200)","v":"mide"}]
[]
[]
[]
[]
[]
[]
[null,"La distancia entre A y B es conocida y también lo son los ángulos α y β. Teniendo en cuenta esto puedo reslolver el triángulo ACB. Y obtengo la distancia entre A y C."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"La distancia entre los dos puntos es:",null,null,null,{"$f":" (L8*SIN(Q14)/(SIN(PI()-Q12-Q14)))","v":{"$error":"#VALUE!"}}]

{"sheet":"ALTURA DE PIE ACCESIBLE","index":3,"n_rows":32,"n_cols":17,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"ALTURA DE PIE ACCESIBLE:"]
[]
[]
[null,null,null,null,null,null,"Medidas que tenemos que tomar:"]
[]
[null,null,null,null,null,null,"Distancia entre los dos puntos de observación A y B: "]
[]
[null,null,null,null,null,null,null,null,"GRADOS CENTESIMALES",null,null,"GRADOS SEXAGESIMALES",null,null,null,null,"RADIANES"]
[]
[null,null,null,null,null,null,"Ángulo α",null,null,null,null,null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"Mide\",\"\"),IF(L12=\"\",\"\",IF(L12*100/90=I12,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"mide\",L12*PI()/180),I12*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Distancia del teodolito al suelo",null,null,null,null,null,null,{"$f":"IF(L14=\"\",\"¿El teodolito está en el suelo?\",\"\")","v":"¿El teodolito está en el suelo?"}]
[]
[]
[]
[]
[]
[]
[null,"La distancia entre A y B es conocida y también lo es el ángulos α. Se trata de resolver un triángulo rectángulo del que conocemos un lado y sus ángulos."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"La altura es:",null,null,null,{"$f":" L8*TAN(Q12)+L14","v":{"$error":"#VALUE!"}}]

{"sheet":"ALTURA DE PIE INACCESIBLE I","index":4,"n_rows":32,"n_cols":17,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"ALTURA DE PIE INACCESIBLE:"]
[]
[]
[null,null,null,null,null,null,"Medidas que tenemos que tomar:"]
[]
[null,null,null,null,null,null,"Distancia entre los dos puntos de observación A y B: "]
[]
[null,null,null,null,null,null,null,null,"GRADOS CENTESIMALES",null,null,"GRADOS SEXAGESIMALES",null,null,null,null,"RADIANES"]
[]
[null,null,null,null,null,null,"Ángulo α",null,null,null,null,null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"Mide\",\"\"),IF(L12=\"\",\"\",IF(L12*100/90=I12,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"mide\",L12*PI()/180),I12*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo β",null,null,null,null,null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"Mide\",\"\"),IF(L14=\"\",\"\",IF(L14*100/90=I14,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"mide\",L14*PI()/180),I14*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(L7=1,IF(I16=\"\",IF(L16=\"\",\"mide\",L16*PI()/180),I16*PI()/200),IF(Q12=\"mide\",\"mide\",PI()-Q12))","v":"mide"}]
[]
[null,null,null,null,null,null,"Distancia del teodolito al suelo",null,null,null,null,null,null,{"$f":"IF(L18=\"\",\"¿El teodolito está en el suelo?\",\"\")","v":"¿El teodolito está en el suelo?"}]
[]
[]
[null,"La distancia entre A y B es conocida y también lo son los ángulos α y β. Teniendo en cuenta esto puedo reslolver el triángulo APB. Y obtengo la distancia entre A y P."]
[null,"Una vez conocida la distancia entre A y P se trata de resolver un triángulo rectángulo OAP, del que se conocen un lado y sus ángulos."]
[]
[]
[]
[]
[]
[null,"La distancia entre A y P es:",null,null,null,{"$f":" L8*SIN(Q14)/SIN(PI()-Q14-Q16)","v":{"$error":"#VALUE!"}}]
[]
[]
[]
[null,"La altura es:",null,null,null,{"$f":" (SIN(Q12)*F28)+L18","v":{"$error":"#VALUE!"}}]

{"sheet":"ALTURA DE PIE INACCESIBLE II","index":5,"n_rows":32,"n_cols":17,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"ALTURA DE PIE INACCESIBLE:"]
[]
[]
[null,null,null,null,null,null,"Medidas que tenemos que tomar:"]
[]
[null,null,null,null,null,null,"Distancia entre los dos puntos de observación A y B: "]
[]
[null,null,null,null,null,null,null,null,"GRADOS CENTESIMALES",null,null,"GRADOS SEXAGESIMALES",null,null,null,null,"RADIANES"]
[]
[null,null,null,null,null,null,"Ángulo α",null,null,null,null,null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"Mide\",\"\"),IF(L12=\"\",\"\",IF(L12*100/90=I12,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"mide\",L12*PI()/180),I12*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo γ",null,null,null,null,null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"Mide\",\"\"),IF(L14=\"\",\"\",IF(L14*100/90=I14,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"mide\",L14*PI()/180),I14*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo β",null,null,null,null,null,null,{"$f":"IF(I16=\"\",IF(L16=\"\",\"Mide\",\"\"),IF(L16=\"\",\"\",IF(L16*100/90=I16,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(L7=1,IF(I16=\"\",IF(L16=\"\",\"mide\",L16*PI()/180),I16*PI()/200),IF(Q12=\"mide\",\"mide\",PI()-Q12))","v":"mide"}]
[]
[null,null,null,null,null,null,"Distancia del teodolito al suelo",null,null,null,null,null,null,{"$f":"IF(L18=\"\",\"¿El teodolito está en el suelo?\",\"\")","v":"¿El teodolito está en el suelo?"}]
[]
[]
[null,"La distancia entre A y B es conocida y también lo son los ángulos γ y β. Teniendo en cuenta esto puedo reslolver el triángulo AOB. Y obtengo la distancia entre A y 0."]
[null,"Una vez conocida la distancia entre A y O se trata de resolver un triángulo rectángulo OAP, del que se conocen un lado y sus ángulos."]
[]
[]
[]
[]
[]
[null,"La distancia entre A y O es:",null,null,null,{"$f":" L8*SIN(Q16)/SIN(PI()-Q14-Q16)","v":{"$error":"#VALUE!"}}]
[]
[]
[]
[null,"La altura es:",null,null,null,{"$f":" (TAN(Q12)*F28)+L18","v":{"$error":"#VALUE!"}}]

{"sheet":"ALTURA DE PIE INACCESIBLE (2)","index":6,"n_rows":32,"n_cols":17,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"ALTURA DE PIE INACCESIBLE EN UNA COTA SUPERIOR:"]
[]
[]
[null,null,null,null,null,null,"Medidas que tenemos que tomar:"]
[]
[null,null,null,null,null,null,"Distancia entre los dos puntos de observación C y D: "]
[]
[null,null,null,null,null,null,null,null,"GRADOS CENTESIMALES",null,null,"GRADOS SEXAGESIMALES",null,null,null,null,"RADIANES"]
[]
[null,null,null,null,null,null,"Ángulo α",null,null,null,null,null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"Mide\",\"\"),IF(L12=\"\",\"\",IF(L12*100/90=I12,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"mide\",L12*PI()/180),I12*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo β",null,null,null,null,null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"Mide\",\"\"),IF(L14=\"\",\"\",IF(L14*100/90=I14,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"mide\",L14*PI()/180),I14*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo γ",null,null,null,null,null,null,{"$f":"IF(I16=\"\",IF(L16=\"\",\"Mide\",\"\"),IF(L16=\"\",\"\",IF(L16*100/90=I16,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I16=\"\",IF(L16=\"\",\"mide\",L16*PI()/180),I16*PI()/200)","v":"mide"}]
[]
[]
[]
[]
[null,"La distancia entre C y D es conocida y también lo son los ángulos γ y β. Teniendo en cuenta esto puedo reslolver el triángulo CDA. Y obtengo la distancia entre D y A."]
[null,"Una vez conocida la distancia entre D y A se trata de resolver un triángulo rectángulo DAB, del que se conocen un lado y sus ángulos."]
[]
[]
[]
[]
[]
[null,"La distancia entre A y D es:",null,null,null,{"$f":" L8*SIN(Q16)/SIN(Q12-Q16)","v":{"$error":"#VALUE!"}}]
[]
[]
[]
[null,"La altura del objeto es :",null,null,null,{"$f":" (SIN(Q12-Q14)*F28/SIN(PI()/2+Q14))","v":{"$error":"#VALUE!"}}]

{"sheet":"ALTURA DE PIE INACCESIBLE (3)","index":7,"n_rows":32,"n_cols":17,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"ALTURA DE PIE INACCESIBLE EN UNA COTA INFERIOR:"]
[]
[]
[null,null,null,null,null,null,"Medidas que tenemos que tomar:"]
[]
[null,null,null,null,null,null,"Distancia entre los dos puntos de observación P y P': "]
[]
[null,null,null,null,null,null,null,null,"GRADOS CENTESIMALES",null,null,"GRADOS SEXAGESIMALES",null,null,null,null,"RADIANES"]
[]
[null,null,null,null,null,null,"Ángulo α",null,null,null,null,null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"Mide\",\"\"),IF(L12=\"\",\"\",IF(L12*100/90=I12,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I12=\"\",IF(L12=\"\",\"mide\",L12*PI()/180),I12*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo β",null,null,null,null,null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"Mide\",\"\"),IF(L14=\"\",\"\",IF(L14*100/90=I14,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I14=\"\",IF(L14=\"\",\"mide\",L14*PI()/180),I14*PI()/200)","v":"mide"}]
[]
[null,null,null,null,null,null,"Ángulo γ",null,null,null,null,null,null,{"$f":"IF(I16=\"\",IF(L16=\"\",\"Mide\",\"\"),IF(L16=\"\",\"\",IF(L16*100/90=I16,\"\",\"Las mediciones no coinciden\")))","v":"Mide"},null,null,{"$f":"IF(I16=\"\",IF(L16=\"\",\"mide\",L16*PI()/180),I16*PI()/200)","v":"mide"}]
[]
[]
[]
[]
[null,"La distancia entre P y P' es conocida y también lo son los ángulos γ y β. Teniendo en cuenta esto puedo reslolver el triángulo PQP'. Y obtengo la distancia entre Q y P."]
[null,"Una vez conocida la distancia entre Q y P se trata de resolver un triángulo rectángulo RQP, del que se conocen un lado y sus ángulos."]
[]
[]
[]
[]
[]
[null,"La distancia entre P y Q es:",null,null,null,{"$f":" L8*SIN(Q16)/SIN(Q14-Q16)","v":{"$error":"#VALUE!"}}]
[]
[]
[]
[null,"La altura del objeto es :",null,null,null,{"$f":" (SIN(Q12+Q14)*F28/SIN(PI()/2-Q12))","v":{"$error":"#VALUE!"}}]