To determine the measure of angle LKJ given the equation \(\tan^{-1}\left(\frac{8.9}{7.7}\right) = x\), let's follow these steps:
1. Calculate the ratio: First, we need to find the value of the fraction \(\frac{8.9}{7.7}\).
2. Find the arctangent of the ratio: Use the inverse tangent (or arctan) to find the angle in radians corresponding to the given ratio. The arctan function will give us an angle \( x \) such that \( \tan(x) = \frac{8.9}{7.7} \).
3. Convert the angle from radians to degrees: In trigonometry, the result from the arctan function is typically in radians. To convert radians to degrees, we use the conversion factor \(\frac{180}{\pi}\).
4. Round the result to the nearest whole degree: Finally, we round the angle to the nearest whole number to find the measure of angle LKJ.
The arctangent of the ratio \(\frac{8.9}{7.7}\) is approximately \(0.857561792357106\) radians.
To convert this angle from radians to degrees:
[tex]\[
0.857561792357106 \times \frac{180}{\pi} \approx 49.13467137373643 \text{ degrees}
\][/tex]
Rounding \(49.13467137373643\) to the nearest whole number, we get:
[tex]\[
49 \text{ degrees}
\][/tex]
Therefore, the measure of angle LKJ is \(49^\circ\).
The correct answer from the given choices is:
[tex]\[
49^\circ
\][/tex]
