Convert each angle measure to degrees, minutes, and seconds. If a...

Question

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b).                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                             
   102.3771°

Accepted Answer

Hey, everyone. Here, we are asked to convert the following angle to degrees minutes and seconds. And we need to round the answer to the nearest second when necessary. Here we are given the angle 158.2441 degrees. Here we have four answer choice options. Answer choice. A 158 degrees, 16 minutes and 28 seconds. Answer B 158 degrees, 14 minutes and 45 seconds. Answer C 158 degrees, 16 minutes and 32 seconds and answer D 158 degrees 14 minutes and 39 seconds. So to begin this problem, we first want to break up our given angle into its whole number and its decimal value. So our given angle becomes 158 degrees plus 0.2441 degrees. And now we need to take this decimal value and convert it to minutes. So we first need to recall the conversion where we know that we have 60 minutes in one degree. So now converting, we have 158 degrees plus 0.2441 multiplied by 60 minutes. And now just multiplying, we have 158 degrees plus 14.646 minutes. And now just like we did with our given angle, we now take our minutes value and break it up into the sum of the whole number and the decibel value. So we have 158 degrees plus 40 minutes plus 0.646 minutes. And now we take the decimal value of our minutes and we need to convert it to seconds. So now we just need to recall that we have 60 seconds in one minute. So converting, we have 158 degrees plus 14 minutes plus 0.646 multiplied by 60 seconds. And now just multiplying, we have 158 degrees plus 14 minutes plus 38.76 seconds. And now the last step is to round our seconds value to the nearest second. And so we see that the 10th place has seven, which is above five. So we round up and so we have 158 degrees plus 14 minutes plus 39 seconds. And with this, we have converted our given angle to degrees minutes and seconds. And so we are left with answer choice. D where again, we have 158 degrees, 14 minutes and 39 seconds. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 102.3771°

Key Concepts

Angle Conversion

Decimal Degrees

Rounding

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