Convert it `47^(@)20`' into radian.

Answer

To convert \( 47^\circ 20' \) into radians, follow these steps:

### Step 1: Convert minutes to degrees
1. We know that \( 1 \text{ degree} = 60 \text{ minutes} \).
2. Therefore, \( 20' \) (minutes) can be converted to degrees by dividing by 60:
\[ 20' = \frac{20}{60} = \frac{1}{3} \text{ degrees} \]

### Step 2: Add the degrees
3. Now, add the degrees from Step 1 to the whole degrees:
\[ 47^\circ + \frac{1}{3}^\circ = 47 + \frac{1}{3} = \frac{141}{3} \text{ degrees} \]

### Step 3: Convert degrees to radians
4. We use the conversion factor \( \frac{\pi \text{ radians}}{180 \text{ degrees}} \) to convert degrees to radians:
\[ \text{Radians} = \frac{141}{3} \times \frac{\pi}{180} \]

### Step 4: Simplify the expression
5. Simplifying the expression:
\[ \text{Radians} = \frac{141\pi}{3 \times 180} = \frac{141\pi}{540} \]

### Step 5: Further simplify
6. We can simplify \( \frac{141}{540} \):
\[ \frac{141}{540} \approx 0.26167 \text{ (approximately)} \]
Thus,
\[ \text{Radians} \approx 0.26167\pi \]

### Final Result
The final result of converting \( 47^\circ 20' \) into radians is approximately:
\[ 0.26167\pi \text{ radians} \]

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