Question

A hiker moves 3 meters east, which is vector A. Then the hiker moves four meters north, which is vector B. The displacement vector is vector C. What angle is created between vectors C and A?

Answer 1

53.1°

Explanation:

The angle created by vector C and vector A is the angle to the horizontal. Use

Tan θ= opposite/adjacent = 4/3, θ= 53.1°.

Answer 2

About 53.13 degrees.

Explanation:

If we draw the path of the hiker, or rather, all three vectors with vector B having its starting point at the end point of vector A, a right triangle is formed. We will most likely be using trigonometric functions to solve this.

vector A is parallel to the x axis (West - East), and vector B is perpendicular, so we'll be using the inverse tangent function to get the angle based on the ratio of the lengths of vector B to vector A, which is
`(4)/(3)`

atan
`((4)/(3)) = 53.13` degrees.

If one would be pedantic, they'd say that the direction we have to go to get from vector C to vector A is clockwise, which is anti-mathematical, the true answer would be -53.13 degrees. Alternatively, whatever 360-53.13 is.