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).                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                             
   ―25.485°

Accepted Answer

Hey, everyone. Here we are asked to convert the following angle to degrees minutes and seconds. Then we need to round the answer to the nearest second when necessary. Here we are given the angle negative 48.795 degrees. Here we have four answer choice options. Answer choice. A negative 48 degrees, 47 minutes and 42 seconds. Answer B negative 48 degrees, 51 minutes and 10 seconds. Answer C negative 48 degrees, 49 minutes and 58 seconds and answer D negative 48 degrees 46 minutes and 35 seconds. Now, before we begin converting our given angle, we first need to break up the angle into the sum of its whole number and its decimal value. So here we also need to factor out the negative sign. So we have the negative quantity of 48 degrees plus 0.795 degrees. And now we want to take the decimal value and convert it from degrees two minutes. So we first need to recall that there are 60 minutes in one degree. And now to convert the decimal value, we just need to multiply it by 60 minutes. And so we have the negative quantity of 48 degrees plus 0.795 multiplied by 60 minutes. And now just simplifying, we have the negative quantity of 48 degrees plus 47.7 minutes. And now we need to take the minutes value and break it up to the sum of the whole number and the decimal value. And so we have the negative quantity of 48 degrees plus 47 minutes plus 0. minutes. And now we take the decimal value of the minutes and convert it to seconds by first recalling that we have 60 seconds in one minute. And so now converting, we have the negative quantity of 48 degrees plus 47 minutes plus 0. multiplied by 60 seconds. And now simplifying our current expression, we have the negative quantity of 48 degrees plus 47 minutes plus 42 seconds. And now we see that our seconds value is already a, a whole number. So we do not need to round to the nearest second. And so the last step is to just factor back in the negative sign. However, we can notice that we only distribute the negative sign to the degrees since we cannot have negative minutes or negative seconds. So we have negative 48 degrees plus minutes and 42 seconds. And with this final expression, here we are left with answer. Choice a where again, we have negative 48 degrees, 47 minutes and 42 seconds. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). ―25.485°