# Problems from Measurement of angles in degrees, minutes and seconds

1. Write $$12$$ and a half degrees in minutes.
2. Write $$4$$ degrees and $$39$$ minutes in seconds.
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### Development:

1. 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:

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

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.

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

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

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

Adding those quantities we will finally have:

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

### Solution:

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