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Sagot :
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]
[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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