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