Problem

Convert the following angle to degrees, minutes, and seconds form. $\alpha=-89.369^{\circ}$
The answer is
(Simplify your answers. Round to the nearest second as needed.)

Answer

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Answer

\(\boxed{-89^\circ 22' 8''}\) is the final answer.

Steps

Step 1 :Given the angle \(\alpha=-89.369^\circ\).

Step 2 :The whole number part of the decimal degree is the degrees, so the degrees are \(-89\).

Step 3 :Next, we multiply the decimal part by 60 to get the minutes. The decimal part is \(0.369\), so the minutes are \(0.369 \times 60 = 22.14\). The whole number part of this result is the minutes, so the minutes are \(22\).

Step 4 :Then, we multiply the decimal part of the minutes by 60 to get the seconds. The decimal part is \(0.14\), so the seconds are \(0.14 \times 60 = 8.4\). We round this to the nearest second to get \(8\) seconds.

Step 5 :Finally, we combine the degrees, minutes, and seconds to express the angle in degrees, minutes, and seconds form. The angle \(\alpha=-89.369^\circ\) is equivalent to \(-89^\circ 22' 8''\).

Step 6 :\(\boxed{-89^\circ 22' 8''}\) is the final answer.

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