Problems from Measurement of angles in degrees, minutes and seconds

Development:

1. First we transform $12$ degrees to minutes and then we will add the half degree in minutes.

$12\text{degrees}=12\text{degrees}\cdot {\displaystyle \frac{60\text{minutes}}{1\text{degree}}}=12\cdot 60\text{minutes}=720\text{minutes}$

${\displaystyle \frac{1}{2}}\text{degree}={\displaystyle \frac{1}{2}}\text{degree}\cdot {\displaystyle \frac{60\text{minutes}}{1\text{degree}}}=30\text{minutes}$

Adding both quantitiesof minutes we have:

$12\text{degrees}+{\displaystyle \frac{1}{2}}\text{degree}=720\text{minutes}+30\text{minutes}=750\text{minutes}$

2. First, we will change $4$ degrees into seconds, and then we will add the $39$ minutes that we will also have changed into seconds.

$4\text{degrees}=4\text{degrees}\cdot {\displaystyle \frac{60\text{minutes}}{1\text{degree}}}\cdot {\displaystyle \frac{60\text{seconds}}{1\text{minute}}}=$

$=4\cdot 60\cdot 60\text{seconds}=14.400\text{seconds}$

$39\text{minutes}=39\text{minutes}\cdot {\displaystyle \frac{60\text{seconds}}{1\text{minute}}}=39\cdot 60\text{seconds}=2.340\text{seconds}$

Adding those quantities we will finally have:

$4\text{degrees}+39\text{minutes}=14.400\text{seconds}+2.340\text{seconds}=16.740\text{seconds}$

Solution:

1. $750\text{minutes}$
2. $16.740\text{seconds}$

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