6. Trigonometría Tri C3S11 Ángulo de anclaje (Lenguaje algebraico) Un poste de alumbrado de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»L«/mi»«mn»1«/mn»«/math» metros de altura debe ser anclado al suelo desde la mitad de su longitud, utilizando un cable de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»L«/mi»«mn»2«/mn»«/math» metros de largo. Considerando que el poste forma un ángulo recto con el suelo, determine el ángulo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«/math» que se forma entre el cable y el suelo.

Observaciones:

-Ingresa las cifras sin unidad de medida

-Utiliza punto para separar las cifras decimales

-Expresa el resultado utilizando el sìmbolo de grado (º) e ingresa 3 cifras después del punto, con aproximación

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Revisemos el desarrollo de la solución del problema:

Si denotamos la altura del poste como «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«/math», la mitad equivale a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»h«/mi»«mn»2«/mn»«/mfrac»«/math» . Además, designaremos como «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»l«/mi»«mi»c«/mi»«/math» la longitud del cable utilizado para el anclaje y como «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«/math» al ángulo formado entre el cable y el suelo. De esta forma se tiene que:

Si calculamos el valor del seno del ángulo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«/math» se tiene que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mo»(«/mo»«mi»§#945;«/mi»«mo»)«/mo»«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»«/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»«mo»=«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfrac»«mi»h«/mi»«mn»2«/mn»«/mfrac»«/mstyle»«mrow»«mi»l«/mi»«mi»c«/mi»«/mrow»«/mfrac»«/math»

Para determinar el valor del ángulo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«/math» es necesario calcular la función inversa de seno. Es decir.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»=«/mo»«mi»a«/mi»«mi»r«/mi»«mi»c«/mi»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mfrac»«mstyle displaystyle=¨true¨»«mfrac»«mi»h«/mi»«mn»2«/mn»«/mfrac»«/mstyle»«mrow»«mi»l«/mi»«mi»c«/mi»«/mrow»«/mfrac»«/math»

En tu calculadora «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mi»r«/mi»«mi»c«/mi»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mo»(«/mo»«mi»c«/mi»«mi»a«/mi»«mi»n«/mi»«mi»t«/mi»«mi»i«/mi»«mi»d«/mi»«mi»a«/mi»«mi»d«/mi»«mo»)«/mo»«/math» corresponde a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mi»e«/mi»«msup»«mi»n«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»(«/mo»«mi»c«/mi»«mi»a«/mi»«mi»n«/mi»«mi»t«/mi»«mi»i«/mi»«mi»d«/mi»«mi»a«/mi»«mi»d«/mi»«mo»)«/mo»«/math»

Finalmente, se tiene que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»=«/mo»«mi»s«/mi»«mi»e«/mi»«msup»«mi»n«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»(«/mo»«mfrac bevelled=¨true¨»«mstyle displaystyle=¨true¨»«mfrac»«mrow»«mo»#«/mo»«mi»L«/mi»«mn»1«/mn»«/mrow»«mn»2«/mn»«/mfrac»«/mstyle»«mrow»«mo»#«/mo»«mi»L«/mi»«mn»2«/mn»«mo»)«/mo»«/mrow»«/mfrac»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«/math»

Reporta y/o califica esta pregunta:

1. Copia este código: Tri. C3. S11.

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

]]> *]]> Al parecer cometiste un error

]]> .- Santiago Sur 24/6

No corresponde a esta pregunta. Al parecer se copió y pegó una observación errónea.-En la pregunta y en la respretroalimentación dice Ht y en la respuesta dice H(t)

En la observación:

Solo el título con negrita Corregido
Quitar la observación de ingresar las cifras sin unidad de medida
Agregar en: "Expresa el resultado utilizando el sìmbolo de grado (º) e ingresa 3 cifras después del punto" sin aproximar. Corregido

En la retroalimentación:

Como sugerencia escribiría el mismo texto, pero en más líneas. Corregido
Falta escribir la respuesta final porque los alumnos cuando hagan el cuestionario no la verán (solo nosotros la vemos al programar) Corregido

Comentarios: Arnoldo 02/06/2016

Realizado-PENDIENTE: Según acuerdos tomados en la serena los decimales deben ser separados por punto no por coma, además debe indicar a cuantos decimales aproximar.

Realizado-Pendiente: Es conveniente especificar que el triángulo es rectángulo.

PENDIENTE: Según acuerdos tomados en la Serena , incluir fotos en las preguntas genera problemas en la plataforma, la sugerencia es programar los triángulos en el tablero de WIRIS y etiquetar puntos.

Realizado-PEndiente: revisar el símbolo utilizado para las tildes

Realizado-PENDIENTE: Reformular pregunta: Determine el ángulo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8736;«/mo»«mi»§#945;«/mi»«mo»=«/mo»«/math» que ..... o. Luego Agregar al cuadro de respuesta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8736;«/mo»«mi»§#945;«/mi»«mo»=«/mo»«/math»

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>asen</mi><mfenced><mfrac><mfenced><mfrac><mi>L1</mi><mn>2</mn></mfrac></mfenced><mi>L2</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>convertir</mi><mfenced><mrow><mfenced><mi>a</mi></mfenced><mo>,</mo><mo>°</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>*</mo></math>]]></correctAnswer><correctAnswer id="2">.-</correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question>