Question

convert the angle measure 83° 57′ 54″ to decimal degrees.

83° 57′ 54″ = □°
(type an integer or decimal rounded to the nearest thousandth as needed.)

Explanation:

Step1: Convert seconds to minutes

We know that \(1' = 60''\), so to convert \(54''\) to minutes, we divide by \(60\).
\(54\div60 = 0.9'\)
Now add this to the existing minutes: \(57' + 0.9' = 57.9'\)

Step2: Convert minutes to degrees

We know that \(1^{\circ}=60'\), so to convert \(57.9'\) to degrees, we divide by \(60\).
\(57.9\div60 = 0.965^{\circ}\)

Step3: Add to the existing degrees

Now add this to the existing degrees: \(83^{\circ}+ 0.965^{\circ}=83.965^{\circ}\)

Answer:

\(83.965\)