An angle of 30 radians is equal to how many degrees?

Options

A. `(pi)/(30)`
B. `(pi)/(6)`
C. `(30)/(pi)`
D. `(5,400)/(pi)`

Explanation

To convert an angle from radians to degrees, we can use the relationship between radians and degrees. The key relationship is:

- \( 360 \) degrees = \( 2\pi \) radians

From this, we can derive that:

- \( 1 \) radian = \( \frac{180}{\pi} \) degrees

Now, let's convert \( 30 \) radians to degrees step by step.

### Step 1: Write down the conversion factor
We know that:
\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \]

### Step 2: Multiply the number of radians by the conversion factor
To find out how many degrees \( 30 \) radians is, we multiply \( 30 \) by the conversion factor:
\[ 30 \text{ radians} = 30 \times \frac{180}{\pi} \text{ degrees} \]

### Step 3: Simplify the expression
Now we can simplify the expression:
\[ 30 \times \frac{180}{\pi} = \frac{5400}{\pi} \text{ degrees} \]

### Step 4: Conclusion
Thus, \( 30 \) radians is equal to:
\[ \frac{5400}{\pi} \text{ degrees} \]

### Final Answer
The angle of \( 30 \) radians is equal to \( \frac{5400}{\pi} \) degrees.

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