QuestionConvert the angle $-80^{\circ} 36^{\prime}$ to decimal degrees.

Studdy Solution

STEP 1

Assumptions1. The given angle is in degrees and minutes notation. . We want to convert this to decimal degree notation.

STEP 2

First, we need to understand the relationship between degrees and minutes. There are60 minutes in a degree. So to convert minutes to degrees, we divide the number of minutes by60.
$Degrees = Minutes /60$

STEP 3

Now, plug in the given value for the minutes to calculate the equivalent degree.
$Degrees =36^{\prime} /60$

STEP 4

Calculate the equivalent degree.
$Degrees =36^{\prime} /60 =0.6^{\circ}$

STEP 5

Now that we have the equivalent degree for the minutes, we can add this to the given degree to find the total angle in decimal degree notation.
$Total\, angle = Given\, degree + Equivalent\, degree$

STEP 6

Plug in the values for the given degree and the equivalent degree to calculate the total angle.
$Total\, angle = -80^{\circ} +0.6^{\circ}$

STEP 7

Calculate the total angle in decimal degree notation.
$Total\, angle = -80^{\circ} +0.6^{\circ} = -79.4^{\circ}$ The angle in decimal degree notation is $-79.4^{\circ}$ .

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