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Question 461835: How can i find the complementary angle of 19(degrees) 35' 44"
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given an angle, its complementary angle is the angle that when added to the given angle results in 90 degrees.
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Therefore, to find the complementary angle for a given angle, just subtract the given angle from 90 degrees.
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So we start with 90 degrees zero minutes and zero seconds and we subtract from it 19 degrees 35 minutes and 44 seconds.
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Begin by "borrowing" one degree from 90 degrees to make it 89 degrees. The borrowed degree contains 60 minutes. So we can write 90 degrees as 89 degrees plus 60 minutes. Next "borrow" one of the 60 minutes. One minute contains 60 seconds. After this borrow we can now write 90 degrees as 89 degrees 59 minutes and 60 seconds. (Notice that if you add them all up the total is 90 degrees.)
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Now you are able to do the subtraction. From 89 degrees 59 minutes 60 seconds subtract 19 degrees 35 minutes and 44 seconds.
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First subtract the seconds. You have 60 seconds minus 44 seconds for an answer of 16 seconds.
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Next subtract the minutes. You have 59 minutes minus 35 minutes or 24 minutes.
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Finally, subtract the degrees. You have 89 degrees minus 19 degrees or 70 degrees.
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Putting these three answers together, the complementary angle for 19 degrees 35 minutes 44 seconds is, therefore, 70 degrees 24 minutes 16 seconds.
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Hope this concept of borrowing is not too confusing. It's similar to borrowing tens in normal subtraction, but in this case you have to borrow 60 minutes (1 degree = 60 minutes) or 60 seconds (one minute = 60 seconds).
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