`(54)/(7)pi` radians is approximately equal to how many degrees?

Options

A. `8^(@)`
B. `694^(@)`
C. `1,389^(@)`
D. `2,777^(@)`

Answer

To convert \(\frac{54}{7} \pi\) radians to degrees, we can use the conversion formula between radians and degrees. The relationship is given by:

\[ \pi \text{ radians} = 180 \text{ degrees} \]

From this, we can derive that:

\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \]

Now, to convert \(\frac{54}{7} \pi\) radians to degrees, we can multiply by the conversion factor:

\[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \]

Substituting \(\frac{54}{7} \pi\) for Radians:

\[ \text{Degrees} = \frac{54}{7} \pi \times \frac{180}{\pi} \]

Here, the \(\pi\) in the numerator and denominator will cancel out:

\[ \text{Degrees} = \frac{54}{7} \times 180 \]

Now, we can simplify this further:

\[ \text{Degrees} = \frac{54 \times 180}{7} \]

Calculating \(54 \times 180\):

\[ 54 \times 180 = 9720 \]

Now, dividing by 7:

\[ \text{Degrees} = \frac{9720}{7} \approx 1388.57 \]

Rounding this to the nearest whole number gives us:

\[ \text{Degrees} \approx 1389 \]

Thus, \(\frac{54}{7} \pi\) radians is approximately equal to \(1389\) degrees.

**Final Answer:** \(1389\) degrees

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