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Question Video: Converting an Angle Measure in Degrees- Minutes- And Seconds to Decimal Degrees Mathematics

Ethan moves in a straight line, then he changes his direction by 15°36′36″. Find this angle in decimal degrees.

02:25

Video Transcript

Ethan moves in a straight line. Then, he changes his direction by 15 degrees, 36 minutes, 36 seconds. Find this angle in decimal degrees.

We’ve been given an angle measured in degrees, minutes, and seconds and asked to convert it to an angle measured purely in degrees, which will be a decimal value. To do this, we first need to recall what we know about these subunits of minutes and seconds. There are 60 minutes in one degree, and just like with time, there are 60 seconds in one minute. It also follows that as there are 60 seconds in a minute and 60 minutes in a degree, there are 60 times 60 — that’s 3,600 — seconds in a degree.

So we need to take this angle of 15 degrees, 36 minutes, and 36 seconds and work out what the minutes and seconds components will be as a decimal. The integer part of the angle measure is 15, so there are 15 whole degrees. There are 36 minutes, which is equivalent to thirty-six sixtieths of a degree. Simplifying this fraction by dividing both the numerator and denominator by six gives six-tenths of a degree, which as a decimal is 0.6 degrees. So we’ve now worked out that the 36 minutes represent 0.6 degrees.

Finally, we consider the seconds. As one degree contains 3,600 seconds, the fraction of a degree represented by these 36 seconds is 36 over 3,600. We can cancel a factor of 36 in both the numerator and denominator. And we find that the simplest form of this fraction is one over 100, which as a decimal is 0.01.

To complete the problem, we add these three values, each measured in degrees, together. And we find that the angle of 15 degrees, 36 minutes, and 36 seconds, in decimal degrees, is 15.61 degrees.

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