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The equation  tan−1⁡(8.97.7)=𝑥 can be used to find the measure of angle LKJ. What is the measure of angle LKJ? Round to the nearest whole degree.

Question

The equation  tan−1⁡(8.97.7)=𝑥 can be used to find the measure of angle LKJ. What is the measure of angle LKJ? Round to the nearest whole degree.

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Solution

To find the measure of angle LKJ, we need to calculate the inverse tangent (tan^-1) of the ratio 8.9/7.7.

Step 1: Calculate the ratio 8.9/7.7 = 1.1558441558441559

Step 2: Find the inverse tangent of this ratio. Most calculators have a function for this, often labeled as "tan^-1" or "atan".

Step 3: Input the ratio into the inverse tangent function to get the angle in radians.

Step 4: Convert the radians to degrees by multiplying by 180/π.

Step 5: Round to the nearest whole degree.

Doing these calculations, we find that the measure of angle LKJ is approximately 49 degrees.

This problem has been solved

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Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.  JK=𝐽𝐾=  ;  JL=𝐽𝐿=  ;  m∠K𝑚∠𝐾  °

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