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).                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    174.255°

Accepted Answer

Hey, everyone. Here, we are asked to convert the following angle to degrees minutes and seconds and around the answer to the nearest second. When necessary. Here we are given the angle 162.245 degrees. Here we have four answer choice options. Answer choice. A 162 degrees, 18 minutes and 13 seconds. Answer B 162 degrees. 14 minutes and 42 seconds. Answer C 162 degrees, 23 minutes and 57 seconds and answer D 162 degrees 24 minutes and 46 seconds. So before we begin converting our given angle, we first want to break up the angle into the sum of its whole number and its decimal value. So breaking up the angle, we have 162 degrees plus 0.245 degrees. And now we need to take the decimal value and convert it from degrees to minutes. So that means we need to recall that we have 60 minutes in one degree. So to convert our decimal value, we just need to multiply it by 60 minutes. So we have 162 degrees plus 0.245 multiplied by 60 minutes. And now simplifying our expression, we have 162 degrees plus 14.7 minutes. And now we repeat a similar process with our minutes value where we first need to break up the value into its whole number and its decimal. So we have 162 degrees plus 14 minutes plus 0.7 minutes. And now we take the decimal value and we need to convert it from minutes to seconds. And so we need to recall that there are 60 seconds in one minute. And so now converting, we have 162 degrees plus minutes plus 0.7 multiplied by 60 seconds. And now just simplifying, we have 162 degrees plus minutes plus 42 seconds. And now we see that our seconds value is already a whole number. So there is no rounding that we need to do. So this is our final answer here. And so we are left with answer choice B where again, we have 162 degrees, 14 minutes and 42 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). 174.255°

Key Concepts

Angle Conversion

Degrees, Minutes, and Seconds (DMS)

Rounding

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