Final answer:
The correct conversion of 69.51° to degrees, minutes, and seconds is 69° 30' 36", which corresponds to option C.
Step-by-step explanation:
The correct answer is option C) 69°30'51". To convert decimal degrees to degrees, minutes, and seconds, we first take the whole number part of the decimal as the degrees. In this case, that is 69°. To find the minutes, we take the remaining decimal part (0.51 in this case) and multiply by 60, since there are 60 minutes in a degree. This gives us 30.6, which means the minutes are 30'. We then take the decimal part of the minutes (0.6) and multiply by 60 again to find the seconds, which results in 36. So, the conversion of 69.51° to degrees, minutes, and seconds is 69° 30' 36", hence option C is the correct answer.
To convert the angle 69.51° to degrees, minutes, and seconds, we need to break it down. The whole number part is the degrees, the decimal part is the minutes, and multiplying the decimal part of the minutes by 60 gives us the seconds.
69.51° = 69° + 0.51°
0.51° × 60 = 30.6 minutes ≈ 30 minutes
0.6 minutes × 60 = 36 seconds ≈ 36 seconds
Therefore, the angle 69.51° is equivalent to 69°30'36".