Perform each calculation. See Example 3. 90° ― 51° 28'

Verified step by step guidance

1. Understand that the problem requires subtracting two angles given in degrees and minutes: \(90^\circ\) and \(51^\circ 28'\).
2. Recall that 1 degree (\(1^\circ\)) equals 60 minutes (\$60'$), so when subtracting, if the minutes in the minuend (top angle) are less than the minutes in the subtrahend (bottom angle), you need to borrow 1 degree (which is 60 minutes) from the degrees part.
3. Since \(90^\circ\) has 0 minutes and \(51^\circ 28'\) has 28 minutes, borrow 1 degree from 90 degrees, converting it to 89 degrees and adding 60 minutes to the 0 minutes, making it \(89^\circ 60'\).
4. Now subtract the degrees and minutes separately: subtract 28 minutes from 60 minutes, and subtract 51 degrees from 89 degrees.
5. Write the final answer in degrees and minutes format, combining the results from the subtraction of degrees and minutes.

Key Concepts

Angle Measurement in Degrees, Minutes, and Seconds

Angles can be expressed in degrees (°), minutes ('), and seconds ("), where 1 degree equals 60 minutes and 1 minute equals 60 seconds. Understanding this notation is essential for performing calculations involving angles given in this format.

Subtraction of Angles in DMS Format

When subtracting angles expressed in degrees, minutes, and seconds (DMS), you must subtract each component separately, borrowing from higher units if necessary. For example, if the seconds in the minuend are less than in the subtrahend, borrow 1 minute (60 seconds) to perform the subtraction.

Conversion Between DMS and Decimal Degrees

Converting angles from degrees, minutes, and seconds to decimal degrees (and vice versa) can simplify calculations. This involves converting minutes and seconds into fractional degrees, which is useful for verifying results or performing more complex trigonometric operations.