solve problem

Question

Find the complementary and supplementary angles    

 

27^°  35^’   15”     The book I use does not show how to work problems like these.

Answer 1

Hi! The trouble here is converting the minutes and seconds of the angles. Complimentary angles total 90 degrees. There are 60 minutes in one degree, so you actually have 89 degrees and 60 minutes. There are 60 seconds in a minute, so now you have 89 degrees, 59 minutes, and 60 seconds. Now you can subtract:

 

89-27 = 62 degrees

59-35 = 24 minutes

60-15 = 45 seconds

 

So the compliment is 62⁰24'45"

 

The same logic happens for the supplement except you have 179 degrees 59 minutes and 60 seconds.

 

179-27 = 152

59-35 = 24

60-15 = 45

 

So the supplement is 152⁰24'45"

 

Hope this helps

 

Mike

Answer 2

Complementary angles are 2 angles that add up to 90^o, so the complementary angle to this one is:

 

90^o - 27^o  37' 15"

 

90^o can also be written 90^o 00' 00' for 90 degrees, zero minutes and zero seconds.  To subtract 15" from 00", we have to borrow from the minutes, so we rewrite 90^o as 89^o 60' 00" and then borrow from the 60', giving us 89^o 59' 60".

 

Subtracting, we get:

 

60" - 15" = 45"

59' - 37' = 22'

89^o - 27^o = 62^o

 

So, the complementary angle to 27^o 37' 15" is 62^o 22' 45"

 

Since supplementary angles add up to 180^o, you would use the same method of borrowing to subtract from 180^o.