Question

Find the complement to an angle measuring 36 degrees 18' 47''. A) 53 degrees 41' 13'' B) 53 degrees 41' 47'' C) 54 degrees 41' 13'' D) 54 degrees 41' 47''

Answer 1

The complement to an angle measuring 36 degrees 18' 47'' is found by firstly converting the given angle and 90 degrees into seconds, subtracting the two, and then converting the result back into degrees, minutes, and seconds (DMS) format. This yields (A) 53 degrees 41' 13''.

Step-by-step explanation:

The question is asking for the complement of an angle. The complement of an angle is obtained by subtracting the given angle from 90 degrees. When dealing with angles measured in degrees, minutes, and seconds (DMS), we first need to convert everything into seconds.

So first, let's convert 90 degrees into seconds. 1 degree is equal to 60 minutes, and 1 minute is equal to 60 seconds. Therefore, 90 degrees is equal to 90*60*60 = 324,000 seconds.

Then, let's convert 36 degrees 18' 47'' into seconds. This amounts to 36*60*60 + 18*60 + 47 = 130,727 seconds.

Now we can find the complement by subtracting the given angle from 90 degrees: 324,000 seconds - 130,727 seconds = 193,273 seconds.

Finally, we convert this result back to DMS. 193,273 seconds is equal to 53 degrees, 41 minutes, and 13 seconds. So the complement of the given angle is 53 degrees, 41 minutes, and 13 seconds. Therefore, the correct answer is (A) 53 degrees 41' 13''.

Learn more about Complementary Angles