Questions: Convert the angle to D° M′ S″ form. Round the answer to the nearest second. 265.43° 265° 25′ 43″ 265° 26′ 47″ 265° 47′ 43″ 265° 25′ 48″

Solution Steps

To convert a decimal degree angle to degrees, minutes, and seconds (D° M' S''), we first separate the whole number part as degrees. Then, we take the decimal part and multiply it by 60 to get the minutes. Finally, we take the decimal part of the minutes and multiply it by 60 to get the seconds. We round the seconds to the nearest whole number.

Given the angle \( 265.43^{\circ} \), we separate the whole number part to find the degrees: \[ \text{Degrees} = 265 \]

Next, we take the decimal part \( 0.43 \) and convert it to minutes by multiplying by \( 60 \): \[ \text{Minutes} = 0.43 \times 60 = 25.8 \] Taking the whole number part, we have: \[ \text{Minutes} = 25 \]

Now, we take the decimal part of the minutes \( 0.8 \) and convert it to seconds by multiplying by \( 60 \): \[ \text{Seconds} = 0.8 \times 60 = 48 \] Rounding to the nearest whole number gives us: \[ \text{Seconds} = 48 \]

Final Answer