Question

Convert 40g 35' 20" into degrees, minutes, and seconds.

Answer 1

To convert the angle measurement of 40° 35' 20" to decimal degrees, the minutes and seconds are first converted into decimal form and then added to the whole degrees, resulting in 40.58889°. Rounded to the tenths place, the final angle is 40.6°.

Step-by-step explanation:

To convert the angle 40° 35' 20" to a decimal in degrees, you first need to understand that 1 degree equals 60 minutes and 1 minute equals 60 seconds. Therefore, the conversion for the angle involves turning the minutes and seconds into a fractional part of a degree. You can do this by following these steps:

1. Convert the seconds into minutes by dividing by 60. In this case, 20" ÷ 60 = 0.3333' (repeating).
2. Add this value to the minutes. Now you have 35' + 0.3333' = 35.3333'.
3. Convert this total number of minutes into degrees by dividing by 60. So, 35.3333' ÷ 60 = 0.58889° (repeating).
4. Add this decimal degree to the whole degrees to get the final answer. Thus, 40° + 0.58889° = 40.58889°.

When rounding to the tenths place based on 35.5 g (which suggests that the least precise measurement we're considering is to the tenths place), the final angle is 40.6°.