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Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.

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Answer to a math question Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.

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Cristian
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Para determinar todas las razones trigonométricas de un triángulo rectángulo, primero necesitamos identificar qué medidas de lados tenemos disponibles: el cateto opuesto (el lado que es perpendicular al ángulo recto) y el cateto adyacente (el lado que forma uno de los ángulos agudos junto al ángulo recto).

A partir de estas medidas, podemos calcular las siguientes razones trigonométricas:

1. El seno del ángulo agudo:
\sin(\theta) = \frac{{\text{{cateto opuesto}}}}{{\text{{hipotenusa}}}}

2. El coseno del ángulo agudo:
\cos(\theta) = \frac{{\text{{cateto adyacente}}}}{{\text{{hipotenusa}}}}

3. La tangente del ángulo agudo:
\tan(\theta) = \frac{{\text{{cateto opuesto}}}}{{\text{{cateto adyacente}}}}

4. La cosecante del ángulo agudo:
\csc(\theta) = \frac{1}{{\sin(\theta)}}

5. La secante del ángulo agudo:
\sec(\theta) = \frac{1}{{\cos(\theta)}}

6. La cotangente del ángulo agudo:
\cot(\theta) = \frac{1}{{\tan(\theta)}}

Recuerda que el ángulo agudo se refiere al ángulo que no es el ángulo recto en el triángulo rectángulo.

En resumen, para determinar las razones trigonométricas de un triángulo rectángulo, necesitamos saber los valores del cateto opuesto y el cateto adyacente. A partir de ahí, podemos calcular el resto de las razones utilizando las fórmulas mencionadas.

\textbf{Respuesta: Las principales razones trigonométricas son el seno, coseno, tangente, cosecante, secante y cotangente del ángulo agudo en el triángulo rectángulo.}

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