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21) Se tiene una fuerza cuyo origen es [tex]$(0, 0)$[/tex] y el extremo forma el siguiente ángulo respecto al eje positivo:

a) [tex]$22^{\circ} 37^{\prime} 11^{\prime \prime}$[/tex]
b) [tex]$67^{\circ} 22^{\prime} 48^{\prime \prime}$[/tex]
c) [tex]$22^{\circ} 67^{\prime} 48^{\prime \prime}$[/tex]
d) [tex]$37^{\circ} 22^{\prime} 11^{\prime \prime}$[/tex]
e) [tex]$11^{\circ} 22^{\prime} 48^{\prime \prime}$[/tex]

Sagot :

GinnyAnswer
Para convertir los ángulos de grados, minutos y segundos (DMS) a grados decimales, usamos la siguiente fórmula:

[tex]\[ \text{Grados decimales} = \text{Grados} + \left( \frac{\text{Minutos}}{60} \right) + \left( \frac{\text{Segundos}}{3600} \right) \][/tex]

Vamos a convertir cada uno de los ángulos proporcionados paso a paso:

### a) \(22^{\circ} 37^{\prime} 11^{\prime \prime}\)

[tex]\[ Grados \, decimales = 22 + \left( \frac{37}{60} \right) + \left( \frac{11}{3600} \right)\\ Grados \, decimales = 22 + 0.6166667 + 0.0030556\\ Grados \, decimales = 22.6197222 \][/tex]

### c) \(22^{\circ} 67^{\prime} 48^{\prime \prime}\)

Considerando que \(67^{\prime} = 1^{\circ} \) y \( 7^{\prime} \) (\(1^{\circ} = 60^{\prime}\)):

[tex]\[ Grados \, decimales = 22 + 1 + \left( \frac{7}{60} \right) + \left( \frac{48}{3600} \right)\\ Grados \, decimales = 22 + 1 + 0.1166667 + 0.0133333\\ Grados \, decimales = 23.13 \][/tex]

### e) \(11^{\circ} 22^{\prime} 48^{\prime \prime}\)

[tex]\[ Grados \, decimales = 11 + \left( \frac{22}{60} \right) + \left( \frac{48}{3600} \right)\\ Grados \, decimales = 11 + 0.3666667 + 0.0133333\\ Grados \, decimales = 11.38 \][/tex]

### b) \(67^{\circ} 22^{\prime} 48^{\prime \prime}\)

[tex]\[ Grados \, decimales = 67 + \left( \frac{22}{60} \right) + \left( \frac{48}{3600} \right)\\ Grados \, decimales = 67 + 0.3666667 + 0.0133333\\ Grados \, decimales = 67.38 \][/tex]

### d) \(37^{\circ} 22^{\prime} 11^{\prime \prime}\)

[tex]\[ Grados \, decimales = 37 + \left( \frac{22}{60} \right) + \left( \frac{11}{3600} \right)\\ Grados \, decimales = 37 + 0.3666667 + 0.0030556\\ Grados \, decimales = 37.3697222 \][/tex]

### Resumen:

Después de convertir todos los ángulos a formato decimal, obtenemos los siguientes resultados:

1. \( 22^{\circ} 37^{\prime} 11^{\prime \prime} \rightarrow 22.6197222 \)
2. \( 22^{\circ} 67^{\prime} 48^{\prime \prime} \rightarrow 23.13 \)
3. \( 11^{\circ} 22^{\prime} 48^{\prime \prime} \rightarrow 11.38 \)
4. \( 67^{\circ} 22^{\prime} 48^{\prime \prime} \rightarrow 67.38 \)
5. \( 37^{\circ} 22^{\prime} 11^{\prime \prime} \rightarrow 37.3697222 \)

Por lo tanto, los ángulos convertidos a grados decimales son:

[tex]\[ [22.6197222, 23.13, 11.38, 67.38, 37.3697222] \][/tex]
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