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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 √°ngulo agudo:
\sin(\theta) = \frac{{\text{{cateto opuesto}}}}{{\text{{hipotenusa}}}}

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

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

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

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

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

Recuerda que el √°ngulo agudo se refiere al √°ngulo que no es el √°ngulo recto en el tri√°ngulo rect√°ngulo.

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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