aConvert the decimal part of the degrees to minutes of arc, then convert the decimal part of the minutes to seconds of arc.
B
b Convert the seconds of arc to minutes of arc. Then add the result to the given minutes and convert this sum to degrees.
A
a70∘33′
B
b110.76∘
Practice makes perfect
a We want to write the angle measure 70.55∘ in the notation using minutes and seconds of arc. Note that we have 70 whole degrees plus an additional decimal part of 0.55 degrees.
70.55∘=70∘+0.55∘
We will convert the decimal part to minutes of arc. If the result is not a whole number, we will convert the remaining decimal part into seconds of arc. First, let's use the conversion factor from degrees to minutes of arc.
1deg60min
We will find the minutes of arc part of the angle measure by multiplying 0.55∘ by this conversion factor.
Since the conversion to minutes of arc resulted in a whole number, we have 0 remaining seconds of arc. Therefore, the angle measure of 70.55∘ written in the notation with minutes and seconds of arc will be 70∘33′.
b To write the angle measure 110∘45′30′′ we will convert the minutes and seconds of arc to degrees. First we will convert the seconds of arc to minutes of arc. This will involve using the conversion factor from seconds to minutes of arc.
60sec1min
Let's multiply 30′′, which can be also written as 30sec, by this conversion factor.
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