QuestionConvert the angle $\alpha=73^{\circ} 39^{\prime} 16^{\prime \prime}$ to decimal degrees.

Studdy Solution

STEP 1

Assumptions1. The given angle is in degrees, minutes, and seconds. . We need to convert this angle to decimal degrees.

STEP 2

The formula to convert an angle from degrees, minutes, and seconds to decimal degrees is $\text{Decimal degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} + \frac{\text{Seconds}}{3600}$

STEP 3

Now, plug in the given values for the degrees, minutes, and seconds into the formula.
$\text{Decimal degrees} =73^{\circ} + \frac{39^{\prime}}{60} + \frac{16^{\prime \prime}}{3600}$

STEP 4

Perform the division to convert the minutes and seconds to decimal degrees.
$\text{Decimal degrees} =73^{\circ} + \frac{39}{60}^{\circ} + \frac{16}{3600}^{\circ}$

STEP 5

Calculate the decimal degrees.
$\text{Decimal degrees} =73^{\circ} +0.65^{\circ} +0.00444^{\circ}$

STEP 6

Add the decimal degrees together.
$\text{Decimal degrees} =73^{\circ} +0.65^{\circ} +0.00444^{\circ} =73.65444^{\circ}$ The angle in decimal degrees is $73.65444^{\circ}$ .

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QuestionConvert the angle $\alpha=73^{\circ} 39^{\prime} 16^{\prime \prime}$ to decimal degrees.

Studdy Solution

STEP 1

Assumptions1. The given angle is in degrees, minutes, and seconds. . We need to convert this angle to decimal degrees.

STEP 2

The formula to convert an angle from degrees, minutes, and seconds to decimal degrees is $\text{Decimal degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} + \frac{\text{Seconds}}{3600}$

STEP 3

Now, plug in the given values for the degrees, minutes, and seconds into the formula.
$\text{Decimal degrees} =73^{\circ} + \frac{39^{\prime}}{60} + \frac{16^{\prime \prime}}{3600}$

STEP 4

Perform the division to convert the minutes and seconds to decimal degrees.
$\text{Decimal degrees} =73^{\circ} + \frac{39}{60}^{\circ} + \frac{16}{3600}^{\circ}$

STEP 5

Calculate the decimal degrees.
$\text{Decimal degrees} =73^{\circ} +0.65^{\circ} +0.00444^{\circ}$

STEP 6

Add the decimal degrees together.
$\text{Decimal degrees} =73^{\circ} +0.65^{\circ} +0.00444^{\circ} =73.65444^{\circ}$ The angle in decimal degrees is $73.65444^{\circ}$ .

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QuestionConvert the angle α=73∘39′16′′\alpha=73^{\circ} 39^{\prime} 16^{\prime \prime}α=73∘39′16′′ to decimal degrees.

Studdy Solution

STEP 1

Assumptions1. The given angle is in degrees, minutes, and seconds. . We need to convert this angle to decimal degrees.

STEP 2

The formula to convert an angle from degrees, minutes, and seconds to decimal degrees isDecimal degrees=Degrees+Minutes60+Seconds3600\text{Decimal degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} + \frac{\text{Seconds}}{3600} Decimal degrees=Degrees+60Minutes​+3600Seconds​

STEP 3

Now, plug in the given values for the degrees, minutes, and seconds into the formula.Decimal degrees=73∘+39′60+16′′3600\text{Decimal degrees} =73^{\circ} + \frac{39^{\prime}}{60} + \frac{16^{\prime \prime}}{3600} Decimal degrees=73∘+6039′​+360016′′​

STEP 4

Perform the division to convert the minutes and seconds to decimal degrees.Decimal degrees=73∘+3960∘+163600∘\text{Decimal degrees} =73^{\circ} + \frac{39}{60}^{\circ} + \frac{16}{3600}^{\circ} Decimal degrees=73∘+6039​∘+360016​∘

STEP 5

Calculate the decimal degrees.Decimal degrees=73∘+0.65∘+0.00444∘\text{Decimal degrees} =73^{\circ} +0.65^{\circ} +0.00444^{\circ} Decimal degrees=73∘+0.65∘+0.00444∘

STEP 6

Add the decimal degrees together.Decimal degrees=73∘+0.65∘+0.00444∘=73.65444∘\text{Decimal degrees} =73^{\circ} +0.65^{\circ} +0.00444^{\circ} =73.65444^{\circ} Decimal degrees=73∘+0.65∘+0.00444∘=73.65444∘The angle in decimal degrees is 73.65444∘73.65444^{\circ}73.65444∘.

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QuestionConvert the angle $\alpha=73^{\circ} 39^{\prime} 16^{\prime \prime}$ to decimal degrees.

The formula to convert an angle from degrees, minutes, and seconds to decimal degrees is $\text{Decimal degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} + \frac{\text{Seconds}}{3600}$

Now, plug in the given values for the degrees, minutes, and seconds into the formula.
$\text{Decimal degrees} =73^{\circ} + \frac{39^{\prime}}{60} + \frac{16^{\prime \prime}}{3600}$

Perform the division to convert the minutes and seconds to decimal degrees.
$\text{Decimal degrees} =73^{\circ} + \frac{39}{60}^{\circ} + \frac{16}{3600}^{\circ}$

Calculate the decimal degrees.
$\text{Decimal degrees} =73^{\circ} +0.65^{\circ} +0.00444^{\circ}$

Add the decimal degrees together.
$\text{Decimal degrees} =73^{\circ} +0.65^{\circ} +0.00444^{\circ} =73.65444^{\circ}$ The angle in decimal degrees is $73.65444^{\circ}$ .