6. Trigonometría Tri C1S01 calcular los catetos (lenguaje algebraico) En un triángulo rectángulo  la hipotenusa mide «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«/math» cm  y  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sin«/mi»«mfenced»«mi»§#945;«/mi»«/mfenced»«/math»=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«/math»  Encuentra la medida de los catetos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«/math».(«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«/math» es el ángulo opuesto al cateto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»).

                                                              

                                  #graf

                                          

 

Observación:

Si el resultado es un número decimal ingresa el valor con punto, y sin unidad de medida., con dos decimales y aproximar (ejemplo 35,6784  ingrese 35.68)

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Para calcular el cateto a y el cateto b debemos aplicar la fórmula del seno del ángulo alfa

 

                                             «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sin«/mi»«mfenced»«mi»§#945;«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»c«/mi»«mi»a«/mi»«mi»t«/mi»«mi»e«/mi»«mi»t«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»p«/mi»«mi»u«/mi»«mi»e«/mi»«mi»s«/mi»«mi»t«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»§#225;«/mi»«mi»n«/mi»«mi»g«/mi»«mi»u«/mi»«mi»l«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»§#945;«/mi»«/mrow»«mrow»«mi»h«/mi»«mi»i«/mi»«mi»p«/mi»«mi»o«/mi»«mi»t«/mi»«mi»e«/mi»«mi»n«/mi»«mi»u«/mi»«mi»s«/mi»«mi»a«/mi»«/mrow»«/mfrac»«/math»

 

 aplicando los datos en la fórmula   

                                                       «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sin«/mi»«mfenced»«mi»§#945;«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mi»a«/mi»«mrow»«mo»#«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/math»

                  

                                                       «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»d«/mi»«mo»=«/mo»«mi»a«/mi»«/math»

 

Entonces                                        cateto a = #sol1 

   

Para hallar el cateto b  reemplazamos en el teorema de pitagoras

 

                                                         «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»c«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«/math»

 

Reemplazando                                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#32;«/mo»«mo»=«/mo»«mo»§#32;«/mo»«mo»#«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mo»§#32;«/mo»«mo»+«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«/math»

 

Despejando                                    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«/math»

                          

                                                       «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mo»#«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«/msqrt»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mi»b«/mi»«/math»

 

                                                       cateto b = #sol2

 

Reporta y/o califica esta pregunta:

 1. Copia este código: Tri. C1. S01. c.

 2. Presiona este enlace, pega el código y completa el formulario

                           

]]> 1 .3333333 0 0 a=#sol1b=#sol2]]> Muy Bien

]]> -]]> Revisemos el procedimiento para mejores resultados n, si aún tienes dudas consulta a tu profesor.

]]> -  

Santiago Sur 24/6

 

En la observación:

 

Debe indicar con cuántos decimales trabajar y la respuesta con cuántos decimales y si se aproxima o no.

corregido.

 

En la retroalimentación:

 

Aparece el valor y debe aparecer la letra de la variable b.  Corregido.

 

 

Observaciones:  N:G:R:

Pendiente : Según acuerdo, en capacitación se indicó que no es conveniente pegar imágenes.Corregido.

Pendiente : Se sugiere normalizar el número de decimales, no es bueno que el enunciado contenga  cuatro decimales y en la respuesta se pidan solo dos.Corregido.

 

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