Sure, let's work through the problem together step-by-step.
Step 1: Understand the Problem
We need to find the measure of angle \( x \) where \( x = \tan^{-1}\left(\frac{8.9}{7.7}\right) \). This involves calculating the arctangent of the given ratio.
Step 2: Calculate the Ratio
First, compute the ratio of the two given numbers:
[tex]\[ \frac{8.9}{7.7} \][/tex]
This fraction simplifies to approximately:
[tex]\[ 1.155844155844156 \][/tex]
Step 3: Calculate the Arctangent
Next, find the arctangent (inverse tangent) of this ratio. The arctangent function, \(\tan^{-1}\), gives the angle whose tangent is the given number. In this case:
[tex]\[ x = \tan^{-1}(1.155844155844156) \][/tex]
[tex]\[ x \approx 0.857561792357106 \][/tex] radians
Step 4: Convert Radians to Degrees
Since angles are often measured in degrees, we convert the result from radians to degrees. We use the conversion factor:
[tex]\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \][/tex]
So,
[tex]\[ x \approx 0.857561792357106 \times \frac{180}{\pi} \][/tex]
[tex]\[ x \approx 49.13467137373643 \text{ degrees} \][/tex]
Step 5: Summarize the Solution
- The ratio \(\frac{8.9}{7.7}\) is approximately 1.155844155844156.
- The arctangent of this ratio is approximately 0.857561792357106 radians.
- Converting this to degrees, the measure of angle \( x \) is approximately 49.13467137373643 degrees.
Therefore, the measure of angle [tex]\( \angle LKJ \)[/tex] is approximately [tex]\( 49.13 \)[/tex] degrees.
