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Trigonometría

1) Considere el triángulo PQR rectángulo en Q. De acuerdo con los datos de la figura adjunta determine el valor de $\\tan{(\\epsilon)}$.

A) $\\LARGE \\frac{8}{15}$

B) $\\LARGE \\frac{15}{17}$

C) $\\LARGE \\frac{15}{8}$

D) $\\LARGE \\frac{17}{15}$

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Recordemos que por definición la $\\tan{\\epsilon}=$$\\Large \\frac{\\text{cateto} \\enspace \\text{opuesto}}{\\text{cateto} \\enspace \\text{adyacente}}$, por lo tanto, al reemplazar los valores de la figura se obtiene:

[[0]]

$\\tan{\\epsilon}=$________

[[1]]

La respuesta es la alternativa: [[2]]

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Trigonometría

2) Considere el triángulo ABC rectángulo en B. De acuerdo con los datos de la figura adjunta determine el valor de $\\text{sen}{(\\delta)}$.

A) $\\LARGE \\frac{5}{4}$

B) $\\LARGE \\frac{3}{4}$

C) $\\LARGE \\frac{3}{5}$

D) $\\LARGE \\frac{4}{5}$

Recordemos que por definición el $\\text{sen}(\\delta)=$$\\Large \\frac{\\text{cateto} \\enspace \\text{opuesto}}{\\text{hipotenusa}}$, por lo tanto, al reemplazar los valores de la figura se obtiene:

[[0]] [[2]]

$\\text{sen}(\\delta)=$________$=$________

[[1]] [[3]]

La respuesta es la alternativa:[[4]]

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3) Si en la figura adjunta el triángulo MNP es rectángulo en N ¿Cuál es el valor de $x$?

A) $16,6$

B) $17,6$

C) $18,4$

D) $19,4$

Para determinar el valor de una razón trigonométrica, usaremos el siguiente link que tiene una calculadora científica, la cual usarás cuando lo indique el profesor:

Calculadora Científica

Ahora usaremos los siguientes pasos, para determinar el valor de $x$ en la figura adjunta:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Paso 1: Determinar que son $15$ y $x$ en la figura, para el triángulo rectángulo en N	\n $15:$[[0]] \n $x:$[[1]] \n
Paso 2: Según lo determinado en el paso 1 debemos escoger la razón trigonométrica a usar:	[[2]]
Paso 3: Escribir la razón [[2]]$(25°)$, según los datos de la figura.	\n \n [[4]] \n [[2]]$(25°)=$_______ \n [[3]] \n
Paso 4: Usar la calculadora dada en el link anterior y determinar con un decimal truncado a la décima el valor de [[2]]$(25°)$.	[[2]]$(25°)=$[[5]]
Paso 5: Despejar la ecuación del paso 3 y determinar el valor de $x$ con un decimal truncado a la décima.	\n \n [[4]] \n $x=$_________$=$[[6]] \n [[5]] \n \n

La respuesta es la alternativa: [[7]]

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4) En la figura adjunta se tiene el triángulo ABC rectángulo en C. Con los datos de la figura determine el valor de $x$.

A) $\\Large \\frac{\\cos(50°)}{10}$

B) $10 \\cdot \\cos{50°}$

C) $\\Large \\frac{10}{\\tan(50°)}$

D) $10 \\cdot \\tan{50°}$

Para resolver este ejercicio seguiremos los siguientes pasos:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Paso 1: Determinar en la figura que son $x$ y $10$, para el triángulo rectángulo en C.

$x=$[[0]]

$10=$[[1]]

Paso 2: Escribir la razón [[2]]$(50°)$, según los datos de la figura

[[4]]

[[2]]$(50°)=$________

[[3]]

Paso 3: Despejar la $x$ en la ecuación, obteniendo que es igual a:

$x=$[[3]]$\\cdot$[[2]]$(50°)$

La respuesta es la alternativa:

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