To find [tex]\(\tan^{-1}(0.52)\)[/tex], we must determine the angle whose tangent is 0.52. This angle can be found in radians and then converted to degrees.
Step 1: Calculate [tex]\(\tan^{-1}(0.52)\)[/tex] in radians.
Given that [tex]\(\tan^{-1}(0.52) \approx 0.4795\)[/tex] radians.
Step 2: Convert the angle from radians to degrees.
The conversion formula from radians to degrees is:
[tex]\[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \][/tex]
Using our calculated radian measure:
[tex]\[ 0.4795 \times \frac{180}{\pi} \approx 27.47^{\circ} \][/tex]
Finally, after rounding 27.47 to one decimal place, we have:
[tex]\[ \tan^{-1}(0.52) \approx 27.5^{\circ} \][/tex]
Therefore, [tex]\(\tan^{-1}(0.52)\)[/tex] in degrees is approximately:
[tex]\[ \boxed{27.5^{\circ}} \][/tex]
So, the correct answer is:
D. [tex]\(27.5^{\circ}\)[/tex]
