Question

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

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

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, $$258^{\circ}\ 39'\ 52''=258.6644^{\circ}$$