Final answer:
The decimal degree value of 45 degrees, 20 minutes, and 30 seconds is 45.3417 degrees, which is achieved by converting minutes and seconds to decimal form and adding them to the whole degrees.
Step-by-step explanation:
The question asks to convert an angle given in degrees, minutes, and seconds to a decimal degree value. To convert minutes and seconds to decimal degrees, we divide the number of minutes by 60 since there are 60 minutes in a degree, and divide the number of seconds by 3600 since there are 60 seconds in a minute and 60 minutes in a degree (60 * 60 = 3600). The angle given is 45 degrees, 20 minutes, and 30 seconds.
To convert 20 minutes to decimal, we calculate 20/60 = 0.33333 degrees. To convert 30 seconds to decimal, we calculate 30/3600 = 0.00833 degrees. Adding these to 45 degrees, we get 45 + 0.33333 + 0.00833 = 45.3417 degrees. Therefore, the degree decimal value of 45 degrees, 20 minutes, and 30 seconds is 45.3417 degrees (option b).