Solve each problem. See Example 6. ...

Question

Solve each problem. See Example 6.                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                      Surveying One student in a surveying class measures an angle as 74.25°, while another student measures the same angle as 74° 20' . Find the difference between these measurements, both to the nearest minute and to the nearest hundredth of a degree.

Accepted Answer

Hey, everyone here, we are asked to find the difference between the two bearings where the first measurement given is 35. degrees. And the other measurement is 35 degrees and 40 minutes. Here we have four answer choice options, answer choice. A three minutes or 0.05 degrees. Answer B four minutes or 0. degrees. Answer C five minutes or 0. degrees and answer D six minutes or 0.01 degrees. So to begin this problem, we want to start by converting 35. degrees into degrees and minutes. So the first step is to break up this value into the sum of its whole number and its decimal value. And so we have 35 degrees plus 0.75 degrees. And now we need to convert the decimal value from degrees into minutes. And so that means we first need to recall that we have 60 minutes in one degree. So now converting, we have 35 degrees plus 0.75 multiplied by minutes. And now just multiplying, we have 35 degrees plus 45 minutes. And so now we have found that 35.75 degrees converts into 35 degrees and minutes. So now we want to find the di difference between our two bearings. And so we have the absolute value of 35 degrees and 45 minutes minus 35 degrees and 40 minutes. And after subtracting, we are just left with the difference of five minutes. And now we just want to move on to finding our difference in degrees. So we need to take 35 degrees and 40 minutes and convert it into just degrees. So first, again, we have 35 degrees plus 40 minutes. And now utilizing our conversion values, we can convert 40 minutes by having 35 degrees plus 40 minutes divided by minutes. And now just simplifying, we have 35 degrees plus 0.6666 degrees. And now just summing our values, we have 35. six degrees. And here we are asked to round our answer to the nearest 100th of a degree. And so we first want to just round our sum here to the nearest 100th. And so we have 35.67 degrees and now we can move on to finding the actual distance. So we have the absolute value of 35.75 degrees minus 35.67 degrees. And now just subtracting, we are left here. With 0.08 degrees. And with this, we have found our difference in both degrees and minutes. And so with these values, we are left with answer choice c where again the difference between the two given bearings are five minutes or 0. degrees. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Solve each problem. See Example 6. Surveying One student in a surveying class measures an angle as 74.25°, while another student measures the same angle as 74° 20' . Find the difference between these measurements, both to the nearest minute and to the nearest hundredth of a degree.