When (2.8) radians is approximately converted into degrees, which value is nearest?

Correct answer: \(160.4^\circ\)

The direct answer is option C, \(160.4^\circ\). A radian measures an angle by comparing arc length with radius. Since a full circle is \(2\pi\) radians and \(360^\circ\), one radian equals \(180/\pi\) degrees, approximately \(57.3^\circ\). Therefore, \(2.8\) radians equals \(2.8\times180/\pi\), or approximately \(2.8\times57.3=160.44^\circ\). The nearest listed value is \(160.4^\circ\). Option A, \(150.4^\circ\), is too small and would result from using an incorrect conversion. Option B, \(155.8^\circ\), is also below the calculated value. Option C is correct because it is closest to \(160.44^\circ\). Option D, \(168.2^\circ\), is too large. Remember: to change radians to degrees, multiply by \(180/\pi\), or approximately by \(57.3\). Do not multiply by \(\pi/180\), because that converts degrees to radians.