Final answer:
The angle 48° 15' 30" is equivalent to 48.258333° when converted to a decimal representation.Therefore, the correct option is: d) 48.258333°
Step-by-step explanation:
To convert the angle 48° 15' 30" to a decimal representation, you need to convert the minutes and seconds to a fraction of a degree. There are 60 minutes in one degree and 60 seconds in one minute. Therefore, 15' is ⅓°, and 30" is ° (½ of a minute or 1/120 of a degree).
The calculation would be as follows:
48° is simply 48 in decimal.To convert 15' to degrees: 15' × (1°/60') = 0.25°.To convert 30" to degrees: 30" × (1'/60") × (1°/60') = 0.008333°.
Adding them up: 48 + 0.25 + 0.008333 = 48.258333°. Hence, the correct decimal representation of the angle 48° 15' 30" is 48.258333°.Therefore, the correct option is: d) 48.258333°