1 radian is approximately equal to

Options

A. `57^(@)16'`
B. `47^(@)18'30''`
C. `53^(@)17'45''`
D. `43^(@)16'`

Answer

To find the approximate value of 1 radian in degrees, we can follow these steps:

### Step 1: Understand the conversion formula
The conversion from radians to degrees is given by the formula:
\[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \]
Since we are looking for the value of 1 radian, we can substitute 1 for radians:
\[ \text{Degrees} = 1 \times \frac{180}{\pi} \]

### Step 2: Use the approximate value of \(\pi\)
The approximate value of \(\pi\) is \( \frac{22}{7} \). So, we can substitute this value into our formula:
\[ \text{Degrees} = 1 \times \frac{180}{\frac{22}{7}} = 1 \times \frac{180 \times 7}{22} \]

### Step 3: Simplify the expression
Now, we simplify the expression:
\[ \text{Degrees} = \frac{1260}{22} \]
Next, we can perform the division:
\[ \text{Degrees} = 57.2727\ldots \]

### Step 4: Convert the decimal into degrees, minutes, and seconds
To convert \(57.2727\ldots\) degrees into degrees, minutes, and seconds:
1. The whole number part is \(57\) degrees.
2. Take the decimal part \(0.2727\ldots\) and multiply it by \(60\) to convert it to minutes:
\[ 0.2727 \times 60 \approx 16.3636\ldots \text{ minutes} \]
The whole number part is \(16\) minutes.
3. Take the decimal part \(0.3636\ldots\) and multiply it by \(60\) to convert it to seconds:
\[ 0.3636 \times 60 \approx 21.8181\ldots \text{ seconds} \]
The whole number part is approximately \(22\) seconds.

### Final Result
Thus, \(1\) radian is approximately equal to:
\[ 57 \text{ degrees } 16 \text{ minutes } 22 \text{ seconds} \]
For practical purposes, we can round this to:
\[ 57 \text{ degrees } 16 \text{ minutes} \]

### Conclusion
Therefore, the answer is:
**1 radian is approximately equal to 57 degrees 16 minutes.**