Question

convert the following angle to degrees, minutes, and seconds form. α = −33.617° the answer is □°□□. (simplify your answers. round to the nearest second as needed.)

Explanation:

Step1: Identify the integer degree part

The given angle is \(\alpha = -33.617^\circ\). The integer part of the degree is \(-33^\circ\). We now focus on the decimal part \(0.617\) to convert it to minutes and seconds.

Step2: Convert decimal degrees to minutes

We know that \(1^\circ = 60'\), so to convert the decimal part \(0.617\) of the degree to minutes, we multiply by \(60\):
\(0.617\times60 = 37.02'\)
The integer part of this result is the number of minutes, so we have \(37'\). Now we focus on the decimal part of the minutes, which is \(0.02\), to convert it to seconds.

Step3: Convert decimal minutes to seconds

We know that \(1' = 60''\), so to convert the decimal part \(0.02\) of the minutes to seconds, we multiply by \(60\):
\(0.02\times60 = 1.2''\)
Rounding to the nearest second, we get \(1''\).

Step4: Combine the parts

Putting it all together, the angle \(-33.617^\circ\) in degrees, minutes, and seconds form is \(-33^\circ37'1''\) (since we round \(1.2''\) to \(1''\)).

Answer:

\(-33^\circ37'1''\)