Question

hw 7: introduction to geometry
score: 14/16 answered: 15/16
question 16
convert the angle 178° 58 28 from degrees/minutes/seconds to decimal degrees rounded to 2 decimal places.
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Explanation:

Step1: Convert seconds to degrees

Since 1 degree = 3600 seconds, then 28 seconds is $\frac{28}{3600}\approx0.0078$ degrees.

Step2: Convert minutes to degrees

Since 1 degree = 60 minutes, then 58 minutes is $\frac{58}{60}\approx0.9667$ degrees.

Step3: Add all parts

The decimal - degree measure is $178 + 0.9667+ 0.0078=178.9745$ degrees.

Step4: Round to 2 decimal places

Rounding 178.9745 to 2 decimal places gives 178.97 degrees.

Answer:

178.97