QuestionConvert the angle $\alpha=18.8211^{\circ}$ to degrees, minutes, and seconds.

Studdy Solution

STEP 1

Assumptions1. The angle is given in decimal degrees as $\alpha=18.8211^{\circ}$ . . We want to convert this to degrees, minutes, and seconds form.

STEP 2

First, we need to separate the degree part from the decimal part. The degree part is the whole number part of the decimal degree.
$\alpha_{degree} = \lfloor \alpha \rfloor = \lfloor18.8211 \rfloor$

STEP 3

Calculate the degree part.
$\alpha_{degree} =18$

STEP 4

Next, we need to find the minute part. This is done by taking the decimal part of the decimal degree, multiplying it by60 (since there are60 minutes in a degree), and then taking the whole number part of the result.
$\alpha_{minute} = \lfloor (\alpha - \alpha_{degree}) \times60 \rfloor = \lfloor (18.8211 -18) \times60 \rfloor$

STEP 5

Calculate the minute part.
$\alpha_{minute} = \lfloor (0.8211) \times60 \rfloor =49$

STEP 6

Finally, we need to find the second part. This is done by taking the decimal part of the minute calculation, multiplying it by60 (since there are60 seconds in a minute), and rounding to the nearest whole number.
$\alpha_{second} = \text{round}((\alpha - \alpha_{degree} - \alpha_{minute}/60) \times3600) = \text{round}((18.8211 -18 -49/60) \times3600)$

STEP 7

Calculate the second part.
$\alpha_{second} = \text{round}((0.0211) \times3600) =76$ So, the angle $\alpha=18.8211^{\circ}$ can be written as $18^{\circ}49'76''$ .

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