The direction of the car's resultant vector is approximately 38.27 degrees west of north.
To find the direction of the car's resultant vector, we can use trigonometry. We have the distances the car travels north and west, and we can treat them as the legs of a right triangle. The resultant vector represents the hypotenuse of this right triangle.
Let's use the following notation:
- Distance traveled north (opposite side) = 87 miles
- Distance traveled west (adjacent side) = 114 miles
- θ (theta) = the angle between the resultant vector and the north direction
We can use the tangent function to find θ:
tan(θ) = (opposite side) / (adjacent side)
tan(θ) = 87 / 114
Now, calculate θ:
θ = arctan(87 / 114)
Using a calculator to find the arctan (inverse tangent) of 87/114, we get:
θ ≈ 38.27 degrees
So, the direction of the car's resultant vector is approximately 38.27 degrees west of north.