Question

5.1
score: 12.83/27 answered: 13/27
question 22
convert the following angle to dms notation. round to the nearest second.
38.6177°
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Explanation:

Step1: Separate the degree part

The degree part is the integer part of the given decimal - degree. For \(38.6177^{\circ}\), the degree \(d = 38^{\circ}\).

Step2: Find the minute part

We use the formula \(m=(x - d)\times60\), where \(x = 38.6177\). So \(m=(38.6177 - 38)\times60=0.6177\times60 = 37.062'\). The minute part \(M\) is the integer part of \(m\), so \(M = 37'\).

Step3: Find the second part

We use the formula \(s=(m - M)\times60\). Since \(m = 37.062\) and \(M = 37\), then \(s=(37.062 - 37)\times60=0.062\times60=3.72''\approx4''\) (rounded to the nearest second).

Answer:

\(38^{\circ}37'4''\)