Answer :
To solve the problem [tex]$36^{\circ} 46^{\prime} 21^{\prime \prime}: 3$[/tex], we start by converting the given angle from degrees, minutes, and seconds into decimal degrees.
1. Convert the angle components to decimal degrees:
- The degrees portion is already given as \(36^\circ\).
- To convert the minutes to degrees, we use the fact that there are 60 minutes in a degree:
[tex]\[ 46 \text{ minutes} = \frac{46}{60} \text{ degrees} = 0.7667 \text{ degrees} \][/tex]
- To convert the seconds to degrees, we use the fact that there are 3600 seconds in a degree:
[tex]\[ 21 \text{ seconds} = \frac{21}{3600} \text{ degrees} = 0.005833 \text{ degrees} \][/tex]
2. Sum all parts to get the total in decimal degrees:
[tex]\[ 36 \text{ degrees} + 0.7667 \text{ degrees} + 0.005833 \text{ degrees} = 36.7725 \text{ degrees} \][/tex]
Now that we have the angle in decimal degrees, we need to divide it by 3.
3. Perform the division:
[tex]\[ 36.7725 \div 3 = 12.2575 \][/tex]
Therefore, the result of dividing \( 36^\circ 46' 21'' \) by 3 is \( 12.2575^\circ \).
To summarize:
- The angle in decimal degrees: \( 36.7725^\circ \)
- The division result: [tex]\( 12.2575^\circ \)[/tex]
1. Convert the angle components to decimal degrees:
- The degrees portion is already given as \(36^\circ\).
- To convert the minutes to degrees, we use the fact that there are 60 minutes in a degree:
[tex]\[ 46 \text{ minutes} = \frac{46}{60} \text{ degrees} = 0.7667 \text{ degrees} \][/tex]
- To convert the seconds to degrees, we use the fact that there are 3600 seconds in a degree:
[tex]\[ 21 \text{ seconds} = \frac{21}{3600} \text{ degrees} = 0.005833 \text{ degrees} \][/tex]
2. Sum all parts to get the total in decimal degrees:
[tex]\[ 36 \text{ degrees} + 0.7667 \text{ degrees} + 0.005833 \text{ degrees} = 36.7725 \text{ degrees} \][/tex]
Now that we have the angle in decimal degrees, we need to divide it by 3.
3. Perform the division:
[tex]\[ 36.7725 \div 3 = 12.2575 \][/tex]
Therefore, the result of dividing \( 36^\circ 46' 21'' \) by 3 is \( 12.2575^\circ \).
To summarize:
- The angle in decimal degrees: \( 36.7725^\circ \)
- The division result: [tex]\( 12.2575^\circ \)[/tex]
