Question

Convert the angle 61 38’ 45” to decimal degrees, and round to the nearest hundredth of a degree

Answer 1

`\text{Decimal degrees} = 61.65^\circ`

Explanation:

We are given the measure of an angle in degrees, minutes and seconds.

We have to convert this measure in decimal degrees.

`\text{Measure of angle =} 61^\circ38'45''`

1 degree equals 60 minutes or 3600 seconds.

The conversion is done with the help of formula:

`\text{Decimal degrees} = d + \displaystyle(m)/(60) + (s)/(3600)\\\\\text{where d is the degree measur, m is the minute measure and s is the second measure.}`

Putting the values, we have:

`\text{Decimal degrees} = d + \displaystyle(m)/(60) + (s)/(3600)\\\\= 61 + (38)/(60) + (45)/(3600) = 61.65^\circ`

Answer 2

A suitable calculator* can do this easily.

61°38'45" = (61 +(38 +45/60)/60)° ≈ 61.65°

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I like the RealCalc app for Android, but many graphing calculators also will do this conversion. Of course, you can simply evaluate the expression as above.