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QuestionCalculate 90∘−41∘57′90^{\circ} - 41^{\circ} 57^{\prime}.

Studdy Solution

STEP 1

Assumptions1. The given angles are in degrees and minutes..1 degree is equal to60 minutes.

STEP 2

First, convert the degrees to minutes for easier subtraction.
90∘=90times60′90^{\circ} =90 \\times60^{\prime}

STEP 3

Calculate the total minutes for90 degrees.
90∘=90times60′=5400′90^{\circ} =90 \\times60^{\prime} =5400^{\prime}

STEP 4

Now, convert the given angle41 degrees57 minutes to minutes.
41∘57′=41times60′+57′41^{\circ}57^{\prime} =41 \\times60^{\prime} +57^{\prime}

STEP 5

Calculate the total minutes for41 degrees57 minutes.
41∘57′=41times60′+57′=2460′+57′=2517′41^{\circ}57^{\prime} =41 \\times60^{\prime} +57^{\prime} =2460^{\prime} +57^{\prime} =2517^{\prime}

STEP 6

Now that we have both angles in minutes, we can subtract them.
5400′−251′5400^{\prime} -251^{\prime}

STEP 7

Calculate the difference in minutes.
5400′−2517′=2883′5400^{\prime} -2517^{\prime} =2883^{\prime}

STEP 8

Now, convert the difference back to degrees and minutes. To do this, divide the total minutes by60 to get the degrees and use the remainder as the minutes.
2883′=2883div60∘2883^{\prime} =2883 \\div60^{\circ}

STEP 9

Calculate the final result in degrees and minutes.
2883′=48∘3′2883^{\prime} =48^{\circ}3^{\prime}So, the result of the calculation 90∘−41∘57′90^{\circ}-41^{\circ}57^{\prime} is 48∘3′48^{\circ}3^{\prime}.

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