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 (h o u r a n g l e) = x (a r c m i n u t e)

Define the base values of the selected units in relation to the SI unit

(r a d i a n)

Left side: 1.0 (h o u r a n g l e) = \frac{π}{12.0} (r a d i a n) = \frac{π}{12.0} (r a d)

Right side: 1.0 (a r c m i n u t e) = \frac{π}{1.08 \times 10^{4}} (r a d i a n) = \frac{π}{1.08 \times 10^{4}} (r a d)

Insert known values into the conversion equation to determine

x

1.0 (h o u r a n g l e) = x (a r c m i n u t e)

Insert known values =>

1.0 \times \frac{π}{12.0} \times (r a d i a n) = x \times \frac{π}{1.08 \times 10^{4}} \times (r a d i a n)

Or

1.0 \cdot \frac{π}{12.0} \cdot (r a d) = x \cdot \frac{π}{1.08 \times 10^{4}} \cdot (r a d)

Cancel SI units

1.0 \times \frac{π}{12.0} \cdot (r a d) = x \times \frac{π}{1.08 \times 10^{4}} \times (r a d)

Conversion Equation

\frac{π}{12.0} = x \times \frac{π}{1.08 \times 10^{4}}

Cancel factors on both sides

Cancel factors

\frac{π}{12.0} = x \times \frac{π}{1.08 \times 10^{4}}

Switch sides

x \times \frac{1.0}{1.08 \times 10^{4}} = \frac{1.0}{12.0}

Isolate

x

Multiply both sides by

(\frac{1.08 \times 10^{4}}{1.0})

x \times \frac{1.0}{1.08 \times 10^{4}} \times \frac{1.08 \times 10^{4}}{1.0} = \frac{1.0}{12.0} \times \frac{1.08 \times 10^{4}}{1.0}

Cancel

x \times \frac{1.0 \times 1.08 \times 10^{4}}{1.08 \times 10^{4} \times 1.0} = \frac{1.0 \times 1.08 \times 10^{4}}{12.0 \times 1.0}

Simplify

x = \frac{1.08 \times 10^{4}}{12.0}

Solve

x

x = 900 = 9 \times 10^{2}

Conversion Equation

1.0 (h o u r a n g l e) = 9 \times 10^{2} (a r c m i n u t e)

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