Question

convert each angle measurement from degrees-minutes-seconds into decimal form. round to the nearest ten - thousandth, if necessary. 15. ( 34 ^ { circ } 14 ^ { prime } 12 ^ { prime prime } ) ( 34.2355 ^ { circ } ) ( 34.5025 ^ { circ } ) ( 34.2367 ^ { circ } ) ( 34.1805 ^ { circ } )

Explanation:

Step1: Convert seconds to minutes

Since \(1' = 60''\), then \(12''=\frac{12}{60}' = 0.2'\).

Step2: Add to existing minutes

Now we have \(14'+ 0.2'=14.2'\).

Step3: Convert minutes to degrees

Since \(1^{\circ}=60'\), then \(14.2'=\frac{14.2}{60}^{\circ}\approx0.2367^{\circ}\).

Step4: Add to existing degrees

\(34^{\circ}+0.2367^{\circ}=34.2367^{\circ}\).

Answer:

\(34.2367^{\circ}\) (the third option)