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.
A. $41^{\circ}$
B. $45^{\circ}$
C. $49^{\circ}$
D. $55^{\circ}$
Answer (2)
Calculate x in radians using the inverse tangent function: x = tan − 1 ( 7.7 8.9 ) ≈ 0.8576 .
Convert x from radians to degrees: x d e g rees = 0.8576 × π 180 ≈ 49.13 .
Round the result to the nearest whole degree: 49.13 ≈ 49 .
The measure of angle LKJ is 4 9 ∘ .
Explanation
Problem Analysis 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 value of x in degrees, rounded to the nearest whole degree.
Calculate x in radians First, we need to calculate the value of x in radians. We have x = tan − 1 ( 7.7 8.9 ) .
The result of this operation is approximately 0.8576 radians.
Convert radians to degrees Next, we convert the angle from radians to degrees using the conversion factor π 180 .
x d e g rees = x r a d ian s × π 180 = 0.8576 × π 180 .
The result of this operation is approximately 49.13 degrees.
Round to the nearest whole degree Finally, we round the angle to the nearest whole degree. Since 49.13 is closer to 49 than to 50, we round down to 49 degrees.
Final Answer Therefore, the measure of angle LKJ is approximately 49 degrees.
Examples
Understanding angles and their measures is crucial in many real-world applications. For example, in construction, architects and engineers use trigonometric functions like tangent to calculate angles for building structures, ensuring stability and precision. Similarly, in navigation, pilots and sailors use angles to determine their course and direction, relying on accurate angle measurements for safe travel. Even in sports, athletes use angles to optimize their performance, such as calculating the launch angle for a basketball shot or the angle of a golf swing.
The measure of angle LKJ is approximately 49 degrees. This is found by calculating tan − 1 ( 7.7 8.9 ) , converting the result from radians to degrees, and rounding to the nearest whole number. Therefore, the answer is 4 9 ∘ .
;
