To determine the measure of angle LKJ using the equation [tex]\(\tan^{-1}\left(\frac{8.9}{7.7}\right)=x\)[/tex], let's break down the steps:
1. Identify the Ratio:
The ratio given inside the inverse tangent function (arctan) is [tex]\(\frac{8.9}{7.7}\)[/tex].
2. Calculate the Ratio:
First, calculate the value of [tex]\(\frac{8.9}{7.7}\)[/tex].
3. Inverse Tangent Function:
Use the arctan (inverse tangent) function, which is denoted as [tex]\(\tan^{-1}\)[/tex], to find the angle whose tangent is [tex]\(\frac{8.9}{7.7}\)[/tex]. This will yield an angle in radians.
4. Convert Radians to Degrees:
After computing the angle in radians, convert this angle to degrees, as most problems expect the angle in degrees.
5. Round the Angle:
Finally, round the angle to the nearest whole degree as required by the problem.
Following these steps to find the measure of angle LKJ, we get [tex]\(49^{\circ}\)[/tex].
Therefore, the answer is [tex]\(49^{\circ}\)[/tex].
