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Ethan moves in a straight line.
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Then, he changes his direction by 15 degrees, 36 minutes, 36 seconds.
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Find this angle in decimal degrees.
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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.
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To do this, we first need to recall what we know about these subunits of minutes and seconds.
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There are 60 minutes in one degree, and just like with time, there are 60 seconds in one minute.
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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.
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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.
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The integer part of the angle measure is 15, so there are 15 whole degrees.
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There are 36 minutes, which is equivalent to thirty-six sixtieths of a degree.
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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.
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So we’ve now worked out that the 36 minutes represent 0.6 degrees.
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Finally, we consider the seconds.
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As one degree contains 3,600 seconds, the fraction of a degree represented by these 36 seconds is 36 over 3,600.
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We can cancel a factor of 36 in both the numerator and denominator.
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And we find that the simplest form of this fraction is one over 100, which as a decimal is 0.01.
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To complete the problem, we add these three values, each measured in degrees, together.
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And we find that the angle of 15 degrees, 36 minutes, and 36 seconds, in decimal degrees, is 15.61 degrees.