Convert each angle measure to decimal degrees. If applicable, rou...

Question

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a).                                                                                                                                                 
                                                                                                                                                                                                                                                                                                                                                                                  
  274° 18' 59"

Accepted Answer

Hey, everyone. Here, we are asked to convert the following angle to decimal degrees and round the answer to three decimal places when necessary. Here we are given 221 degrees, 23 minutes and 51 seconds. Here we have four answer choice options. Answer choice. A 221. degrees. Answer B 221.278 degrees. Answer C 221.429 degrees and answer D 221.398 degrees. So before we begin converting our given angle, we first need to recall the converting values. And so we first recall that there are 60 minutes in, in one degree. And then we also have 3600 seconds in one degree. So in order to convert our minutes and seconds into degrees, we just need to divide the values by either the minutes or seconds converting values. So doing this, our expression becomes 221 degrees plus 23 divided by degrees plus 51 divided by 3600 degrees. And now we just need to divide both of the values. So we have 221 degrees plus 0. degrees plus 0.0142 degrees. And now we just need to start summing the values. So we have 221. degrees. And lastly, we need to round this answer to three decimal places. So here we see that we need to round up the 7 to 8. So our final value is 221. degrees. And with this final rounded answer, we are left with answer choice D where again we have 221.398 degrees. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 274° 18' 59"

Key Concepts

Degrees, Minutes, and Seconds (DMS)

Conversion to Decimal Degrees

Rounding Numbers

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