Measurement of angles in degrees, minutes and seconds

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

$$12 \ \mbox{degrees} = 12 \ \mbox{degrees} \cdot \dfrac{60 \ \mbox{minutes}}{1 \ \mbox{degree}} = 12 \cdot 60 \ \mbox{minutes} = 720 \ \mbox{minutes}$$

$$\dfrac{1}{2} \ \mbox{degree} = \dfrac{1}{2} \ \mbox{degree} \cdot \dfrac{60 \ \mbox{minutes}}{1 \ \mbox{degree}} = 30 \ \mbox{minutes}$$

Adding both quantitiesof minutes we have:

$$12 \ \mbox{degrees} + \dfrac{1}{2} \ \mbox{degree} = 720 \ \mbox{minutes} + 30 \ \mbox{minutes}=750 \ \mbox{minutes}$$

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

$$4 \ \mbox{degrees} = 4 \ \mbox{degrees} \cdot \dfrac{60 \ \mbox{minutes}}{1 \ \mbox{degree}}\cdot \dfrac{60 \ \mbox{seconds}}{1 \ \mbox{minute}} =$$

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

$$39 \ \mbox{minutes} = 39 \ \mbox{minutes} \cdot \dfrac{60 \ \mbox{seconds}}{1 \ \mbox{minute}} = 39 \cdot 60 \ \mbox{seconds} = 2.340 \ \mbox{seconds}$$

Adding those quantities we will finally have:

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