Question

Express the angle as a decimal, to the nearest ten-thousandth of a degree. 258^{\circ}\ 39'\ 52''

Decimals
ANSWERED
asked 2021-05-21
Express the angle as a decimal, to the nearest ten-thousandth of a degree.
\(258^{\circ}\ 39'\ 52''\)

Answers (1)

2021-05-22
Step 1
Use the unitary method to convert the minutes and seconds into decimals.
\(39'=39\ min\)
\(=\left(\frac{39}{60}\right)^{\circ}\)
\(=0.65^{\circ}\)
\(52''=52\ sec\)
\(=\left(\frac{52}{60\ \times\ 60}\right)^{\circ}\)
\(=0.01444^{\circ}\)
Step 2
Now, convert the angle into decimals.
\(258^{\circ}\ 39'\ 52''=258^{\circ}+0.65^{\circ}+0.01444^{\circ}\)
\(=258.66444^{\circ}\)
\(\approx258.6644^{\circ}\)
Hence, \(258^{\circ}\ 39'\ 52''=258.6644^{\circ}\)
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