Convert hour angle to arc minute
Learn how to convert
1
hour angle to
arc minute
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(hour \text{ } angle\right)={\color{rgb(20,165,174)} x}\left(arc \text{ } minute\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(radian\right)\)
\(\text{Left side: 1.0 } \left(hour \text{ } angle\right) = {\color{rgb(89,182,91)} \dfrac{π}{12.0}\left(radian\right)} = {\color{rgb(89,182,91)} \dfrac{π}{12.0}\left(rad\right)}\)
\(\text{Right side: 1.0 } \left(arc \text{ } minute\right) = {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}\left(radian\right)} = {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}\left(rad\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(hour \text{ } angle\right)={\color{rgb(20,165,174)} x}\left(arc \text{ } minute\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{12.0}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}}} \times {\color{rgb(125,164,120)} \left(radian\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{12.0}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(125,164,120)} \left(rad\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{12.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{π}{12.0} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{1.08 \times 10^{4}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{12.0} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{1.08 \times 10^{4}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.08 \times 10^{4}} = \dfrac{1.0}{12.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.08 \times 10^{4}}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.08 \times 10^{4}} \times \dfrac{1.08 \times 10^{4}}{1.0} = \dfrac{1.0}{12.0} \times \dfrac{1.08 \times 10^{4}}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{1.08}} \times {\color{rgb(166,218,227)} \cancel{10^{4}}}}{{\color{rgb(99,194,222)} \cancel{1.08}} \times {\color{rgb(166,218,227)} \cancel{10^{4}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 1.08 \times 10^{4}}{12.0 \times {\color{rgb(255,204,153)} \cancel{1.0}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.08 \times 10^{4}}{12.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 900 = 9 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(hour \text{ } angle\right) = {\color{rgb(20,165,174)} 9 \times 10^{2}}\left(arc \text{ } minute\right)\)
