Question

Convert the angle 45°29'13" to decimal degrees, and round to the nearest hundredth of a degree.

a) 45.50°
b) 45.49°
c) 45.55°
d) 45.45°

Answer 1

To convert the angle 45°29'13" to decimal degrees, we add the degrees to the minutes divided by 60 and the seconds divided by 3600, resulting in 45.4869°. After rounding to the nearest hundredth, the answer is 45.49°, option b).

Step-by-step explanation:

The student is asking to convert the angle 45°29'13" into decimal degrees and round to the nearest hundredth of a degree. To convert from degrees, minutes, and seconds to decimal degrees, we follow these steps:

• Keep the degrees as they are.
• Divide the minutes by 60 and add to the degrees.
• Divide the seconds by 3600 (which is 60*60) and add to the degrees.

In this case, we have:

45° + (29/60)° + (13/3600)°
= 45° + 0.4833° + 0.0036°
= 45.4869°

Rounding to the nearest hundredth of a degree, we get 45.49°. So, the correct answer is b) 45.49°.