William W. answered • 04/14/19
Just to make sure you understand the question, if it said to "Express 45° in terms of a right angle", what would you say? Obviously that would be 1/2 of a right angle. So, to get the answer, we need to divide the angle measure by 90° (45/90 = 1/2).
To do so however, requires a decimal form of the angle instead of the degree/minutes/seconds form. To convert it, you must realize that there are 60 minutes in one degree and 60 seconds in one minute. Since we want everything in terms of degrees, instead of thinking about there being 60 seconds in one minute, lets combine that with the "60 minutes in one degree" to make 3600 seconds in one degree.
Now, take the 17 minutes and convert to degrees by dividing 17 by 60: 17/60 = 0.2833333
Now take the 25 seconds and convert it to degrees by dividing the 25 by 3600: 25/3600 = 0.0069444.
Add the 0.2833333 and the 0.0069444.to the 63 degrees: 63 + 0.2833333 + 0.0069444 = 63.2902777
Now divide the 63.2902777 by 90: 63.2902777/90 = 0.7032253 of a right angle. At this point, you could round, or perhaps turn it to a percent (70.3% of a right angle).
To keep it as a fraction, you would need to get a common denominator and add 63 + 17/60 + 25/3600 = 45569/720 (reduced from 227845/3600) so it would be 45569/720/90 = 45569/64800 of a right angle