The equation $\tan ^{-1}\left(\frac{8.9}{7.7}\right)=x$ can be used to find the measure of angle LKJ. What is the measure of angle LKJ? Round to the nearest whole degree.
Answer (2)
The measure of angle LKJ is approximately 49 degrees, calculated using the arctangent function and converted from radians to degrees. After rounding, the final answer is 49 degrees. This result was obtained from evaluating tan − 1 ( 7.7 8.9 ) .
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Calculate the value of x using the arctangent function: x = tan − 1 ( 7.7 8.9 ) .
Convert the result from radians to degrees using the formula: degrees = radians * π 180 .
Round the result to the nearest whole degree.
The measure of angle LKJ is approximately 4 9 ∘ .
Explanation
Analyze the problem We are given the equation tan − 1 ( 7.7 8.9 ) = x , which represents the angle whose tangent is 7.7 8.9 . Our goal is to find the measure of angle LKJ, which is represented by x , in degrees, rounded to the nearest whole degree.
Calculate x in radians First, we need to calculate the value of x in radians using the arctangent function: x = tan − 1 ( 7.7 8.9 )
Convert radians to degrees Next, we convert the result from radians to degrees using the formula: degrees = radians × π 180 Using a calculator, we find that: x = tan − 1 ( 7.7 8.9 ) ≈ 0.857 radians degrees = 0.857 × π 180 ≈ 49.1 3 ∘
Round to the nearest whole degree Finally, we round the result to the nearest whole degree: 49.1 3 ∘ ≈ 4 9 ∘ Therefore, the measure of angle LKJ is approximately 4 9 ∘ .
State the final answer The measure of angle LKJ, rounded to the nearest whole degree, is 4 9 ∘ .
Examples
Understanding angles and their measures using trigonometric functions like arctangent is crucial in various real-world applications. For instance, in navigation, pilots and sailors use angles to determine their course and direction. Similarly, in construction and engineering, accurate angle measurements are essential for building stable and precise structures. Architects also rely on angles to design aesthetically pleasing and functional buildings. Even in fields like computer graphics and video game development, angles play a vital role in creating realistic and immersive environments.
