Answer:
5° 20' 30" is approximately equal to 0.09216 radians.
Step-by-step explanation:
To convert degrees, minutes, and seconds to radians, we need to convert each unit to its equivalent in radians and then sum them up.
1 degree (°) = π/180 radians
1 minute (') = 1/60 degree = (1/60) * (π/180) radians
1 second (") = 1/60 minute = (1/60) * [(1/60) * (π/180)] radians
Let's calculate the conversion:
5° = 5 * (π/180) radians
20' = 20 * [(1/60) * (π/180)] radians
30" = 30 * [(1/60) * [(1/60) * (π/180)]] radians
Now we can add up these values to get the total in radians:
5° 20' 30" = 5 * (π/180) + 20 * [(1/60) * (π/180)] + 30 * [(1/60) * [(1/60) * (π/180)]]
Simplifying the expression:
5° 20' 30" = (5π/180) + (20π/180*60) + (30π/180*60*60)
Now we can evaluate the expression to find the value in radians:
5° 20' 30" ≈ 0.09216 radians (rounded to five decimal places)