ࡱ> [ B=bjbj ΐΐ%  SSSSSggg8dDg$<GG"iii#######$%(\#uSY |Y Y #SSii^${#{#{#Y SiSi#{#Y #{#{#{#i@g {##t$0${#(!*({#(S{#4,{#>##"|$Y Y Y Y (  : TEMA 7-8: SEMEJANZA-TRIGONOMETRIA. RESUELVE Y COMPRUEBA Ejercicio n 1.- En un mapa, dos poblaciones aparecen separadas 7,5 cm. Cul ser la escala de ese mapa si la distancia real entre ambas poblaciones es de 153 km? En ese mismo mapa, cul sera la distancia real entre dos poblaciones que distan 12,25 cm? Solucin: En este mapa, 7,5 cm representan 153 km reales. 7,5 cm 153 km = 15 300 000 cm  La escala es 1:2 040 000. Si en el mapa hay dos poblaciones que distan 12,25 cm, la distancia real ser: 12,25 2 040 000 = 24 990 000 cm = 249,9 km Ejercicio n 2.- Dos caminos paralelos se unen entre s por dos puentes, que a su vez se cortan en el punto O. Teniendo en cuenta las medidas de la figura, calcula la longitud de los dos puentes.  Solucin: La longitud de un puente ser x + 10,2; la del otro, y + 6,5; por tanto, el objetivo est en calcular el valor de x e y. Los tringulos que se forman son semejantes (sus tres ngulos son iguales) y son:  Se cumple, pues, la proporcionalidad entre lados respectivos:  Las longitudes de los puentes son: 6,8 + 10,2 = 17 m y 9,75 + 6,5 = 16,25 m.  Ejercicio n 3.- Halla las razones trigonomtricas de los ngulos a y b del tringulo ABC sabiendo que es rectngulo. Solucin: Sea x la longitud de la hipotenusa; por el teorema de Pitgoras: 12,962 + 17,282 = x2 x2 = 466,56 x = 21,6 cm Calculamos las razones trigonomtricas de a y b:   Ejercicio n 4.- Sin usar calculadora, completa la siguiente tabla (0 a 90):  Solucin:  Ejercicio n 5.-  Solucin:   Ejercicio n 6.-  Solucin:     Ejercicio n 7.- Representa en la circunferencia goniomtrica sen 150, cos 150 y tg 150. Calcula el valor de cada una de ellas relacionando el ngulo de 150 con un ngulo del primer cuadrante. Solucin: En la circunferencia goniomtrica observamos:   Ejercicio n 8.- Carlos sube por una rampa de 35 m hasta el tejado de su casa. Estando ah, mide la visual entre su casa y la rampa, resultando ser de 70. Calcula la altura de la casa de Carlos y el ngulo que hay entre la rampa y el !78>?P@ A B K |     wiWIWIWh3CJOJQJ^JaJ"h3CJOJQJ^JaJmH sH h3CJOJQJ^JaJ&h356CJOJQJ\]^JaJ&hlh35CJOJQJ\^JaJ hl5CJOJQJ\^JaJ h35CJOJQJ\^JaJ)h356>*CJOJQJ\]^JaJh3OJQJh3CJaJ h3aJhyMOJQJaJh3OJQJaJ8?PA B L | 6 : r  l n p      d1$7$8$H$1$7$8$H$ & ( 6 8 : \ ` f h $ & , . 6 8 > @ F H V X p J L ܼzfzQ)jhlhlCJOJQJU^JaJ&h356CJOJQJ\]^JaJ h35CJOJQJ\^JaJ)h356>*CJOJQJ\]^JaJh3CJOJQJ^JaJh3CJOJQJ^JaJh3CJOJQJ^JaJ#jh3CJOJQJU^JaJ"h3CJOJQJ^JaJmH sH "h3CJOJQJ^JaJmH sH     X Z \ ^  FH"ʼNN<|tlW)h 56>*CJOJQJ\]^JaJhfjgOJQJhfjgCJaJjhfjgUmHnHu#jpJh3CJOJQJU^JaJ#jT0h3CJOJQJU^JaJh3CJOJQJ^JaJh3CJOJQJ^JaJ&h356CJOJQJ\]^JaJ h35CJOJQJ\^JaJ h36CJOJQJ]^JaJ DFJ(z~ d1$7$8$H$^gdfjg ddh1$7$8$H$gdfjg d1$7$8$H$gdfjg 1$7$8$H$gdfjg1$7$8$H$"($&hjtvzȴٴٴxxxxxxxxhfjgCJOJQJ^JaJhfjgCJH*OJQJ^JaJ hfjg6CJOJQJ]^JaJhfjgCJOJQJ^JaJ&hfjg56CJOJQJ\]^JaJ hfjg5CJOJQJ\^JaJ hfjg5CJOJQJ\^JaJ)hfjg56>*CJOJQJ\]^JaJ)z| "(,2468LNPRT߸lXXFX#j_]hfjgCJOJQJU^JaJ&hfjg56CJOJQJ\]^JaJ)jVhhfjgCJOJQJU^JaJ hfjg5CJOJQJ\^JaJ hfjg5CJOJQJ\^JaJ)hfjg56>*CJOJQJ\]^JaJ)h 56>*CJOJQJ\]^JaJ#jRhfjgCJOJQJU^JaJhfjgCJOJQJ^JaJ#jNhfjgCJOJQJU^JaJ0268LPRTvz|~ fd1$7$8$H$gdfjg 1$7$8$H$gdfjg d1$7$8$H$gdfjgTpvxz~òm[I7#jwhfjgCJOJQJU^JaJ#jtshfjgCJOJQJU^JaJ#johfjgCJOJQJU^JaJ#j7jhfjgCJOJQJU^JaJhfjgCJOJQJ^JaJ&hfjg56CJOJQJ\]^JaJ hfjg5CJOJQJ\^JaJ hfjg6CJOJQJ]^JaJ#j-fhfjgCJOJQJU^JaJ)hfjg56>*CJOJQJ\]^JaJ)h 56>*CJOJQJ\]^JaJ^  $ d1$7$8$H$a$gdfjg 1$7$8$H$gdfjg d1$7$8$H$gdfjgpx~<>߻ߦl[l[l[[Jl hfjg6CJOJQJ]^JaJ hfjg5CJOJQJ\^JaJ&hfjg56CJOJQJ\]^JaJ hfjg5CJOJQJ\^JaJ)h 56>*CJOJQJ\]^JaJ)hfjg56>*CJOJQJ\]^JaJ#jQhfjgCJOJQJU^JaJ#jYhfjgCJOJQJU^JaJhfjgCJOJQJ^JaJ#j{hfjgCJOJQJU^JaJ $(DHJ\^2 222"2&2(2>2@2x2Ϻϫs_M< hfjg6CJOJQJ]^JaJ#jhfjgCJOJQJU^JaJ&hfjg56CJOJQJ\]^JaJ&hhfjg5CJOJQJ\^JaJU hfjg5CJOJQJ\^JaJ hfjg5CJOJQJ\^JaJhfjg>*CJOJQJ^JaJ)h 56>*CJOJQJ\]^JaJ)hfjg56>*CJOJQJ\]^JaJhfjgCJOJQJ^JaJjhfjgUmHnHu "$&(J22$2&2*2222D3F3J3$ d1$7$8$H$a$gdfjg d1$7$8$H$gdfjg 1$7$8$H$gdfjgsuelo. Solucin:  Llamamos h a la altura de la casa y a al ngulo que hay entre la rampa y el suelo. Calculamos a: 90 + 70 + a = 180 a = 20  h = 11,9 m es la altura de la casa de Carlos. Ejercicio n 9.- Se quiere medir la altura de una estatua colocada en el centro de un lago circular. Para ello, se mide la visual al extremo superior de la estatua desde el borde del lago y resulta ser de 50; nos alejamos 45 dm y volvemos a medir la visual, obteniendo un ngulo de 35. Averigua la altura de la estatua y la superficie del lago.  Solucin: Hacemos una representacin. Llamamos: h altura de la estatua x radio del lago   Luego h = 64,29 1,19 = 76,51 dm = 7,65 m Calculamos la superficie del lago circular:  La superficie del lago es de 129,78 m2. Ejercicio n 10.- Dos ambulancias, distanciadas 8 km en lnea recta, reciben una llamada de urgencia de una casa. Observa la figura y calcula la distancia que separa a cada ambulancia de la casa:  Solucin: Trazando la altura desde la casa al lado AB, conseguimos dos tringulos rectngulos: CHA y CHB.  Del dibujo deducimos:    De este modo hemos calculado el valor de los catetos en ambos tringulos rectngulos. Aplicando el teorema de Pitgoras, obtendremos la hipotenusa en cada caso:   La ambulancia A est a 5,36 km de la casa, y la ambulancia B, a 5,66 km.     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