Final answer:
To calculate the x- and y-components of the vector (8.0 km, 23 degrees left of y-axis), trigonometric functions are used resulting in an x-component of approximately 7.51 km and a y-component of approximately 7.37 km.
Step-by-step explanation:
To find the x- and y-components of the vector δ→ = (8.0 km, 23 degrees left of y-axis), we use trigonometric functions. Since the angle is given relative to the y-axis, we can consider this as a rotation in the clockwise direction from the negative y-axis.
For the y-component (δy):
- δy = δ cos(θ)
- δy = 8.0 km * cos(23°)
- δy ≈ 7.37 km (since cos(23°) ≈ 0.921)
For the x-component (δx):
- The angle with the x-axis is 90° - 23° = 67°
- δx = δ sin(θ)
- δx = 8.0 km * sin(67°)
- δx ≈ 7.51 km (since sin(67°) ≈ 0.9397)
Therefore, the x-component of the vector is approximately 7.51 km, and the y-component is approximately 7.37 km.