Convert the following angle to decimal degrees.
\[
\alpha=74^{\circ} 51^{\prime} 49^{\prime \prime}
\]
$\alpha \approx$
(Round to 3 decimal places as needed)
Final Answer: The decimal degree representation of the angle \(\alpha=74^\circ 51^\prime 49^\prime \prime\) is \(\boxed{74.864}\) degrees
Step 1 :The given angle is in degrees, minutes, and seconds. To convert this to decimal degrees, we need to convert the minutes and seconds to degrees.
Step 2 :1 degree is equal to 60 minutes and 1 minute is equal to 60 seconds. Therefore, 1 degree is equal to 3600 seconds.
Step 3 :So, to convert minutes to degrees, we divide the number of minutes by 60. To convert seconds to degrees, we divide the number of seconds by 3600.
Step 4 :Given: degrees = 74, minutes = 51, seconds = 49
Step 5 :Converting minutes to degrees: \(\frac{51}{60} = 0.85\) degrees
Step 6 :Converting seconds to degrees: \(\frac{49}{3600} = 0.01361111111111111\) degrees
Step 7 :Adding all the degrees together: \(74 + 0.85 + 0.01361111111111111 = 74.864\) degrees
Step 8 :Final Answer: The decimal degree representation of the angle \(\alpha=74^\circ 51^\prime 49^\prime \prime\) is \(\boxed{74.864}\) degrees