Madison M. answered • 11/16/14
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Complimentary angles are two angles that add up to equal 90°.
(a) is written in degree-minute-second form, so it will be easiest to convert this value to degree-decimal form before finding its complimentary angle.
You can do this two ways:
1. If you know how, plug the angle in DMS form into your calculator and press "enter" to get the decimal form, or
2. Use the following equation:
(seconds/3600) + (minutes/60) + degrees
Where 38 = seconds, 11 = minutes, and 6 = degrees
Either method will give you a degree decimal equal to 6.1939°.
Next is the easy part. Simply subtract this value from 90° to find the compliment.
90° - 6.1939° = 83.8061°
Now you just need to convert this value into DMS mode. You can do this on your calculator by typing in the decimal value, then going to "Second" -> "Angle" -> DMS.
If you need to know the formula, here's how you do it:
1. The "83" part of the decimal degree will remain the degree, so write it down and subtract 83 from the rest of the decimal. You now have 83° ?' ?".
2. Take the remaining decimal (0.8061) and multiply it by 60 to get 48.3666. The whole number value, "48," is the minute value. You now have 83°48' ?".
3. The remaining decimal (0.3666) should now be multiplied by 60 to get the seconds value. This will give you
83°48'22" as your answer.
(b) This one is much simpler because you don't have to convert back and forth from DMS mode.
Simply subtract 38.8° from 90° to get the complimentary angle.
90° - 38.8° = 51.2°
