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------------------------------------------------ A vector has an x-component of length 5 and a y-component of length 4. What is the angle of the vector?

(Hint: Use the inverse tangent.)

A. 51.4 degrees
B. 36.9 degrees
C. 38.7 degrees
D. 53.2 degrees

Using the inverse tangent formula θ = tan^-1(y/x) with the given vector's x-component of length 5 and y-component of length 4, the corresponding angle is approximately 38.7 degrees. Therefore, the answer is c. 38.7 degrees.

Explanation:

In this problem, to find the angle of the vector, we need to use the inverse tangent (also known as tangent-1 or arctan). Specifically, we use the y-component of length 4 and the vector's x-component of length 5.

The formula is given by θ = tan^-1(y/x). Substituting the given values we get, θ = tan^-1(4/5). When you calculate the inverse tangent of (4/5), you get approximately 38.7 degrees. So, the correct answer is c. 38.7 degrees.

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