Final answer:
The length of the x-component of the vector is found by multiplying the magnitude of the vector (8 units) by the cosine of the angle (71°). After performing the calculation, the x-component is approximately 2.6 units, matching answer option A.
Step-by-step explanation:
To determine the length of the x-component of a vector, we can use trigonometric functions. Specifically, we use the cosine of the angle that the vector makes with the x-axis. Given an angle of 71° and a vector length of 8 units (as per the question), the x-component of the vector (Ax) is calculated using the formula:
Ax = A cos θ,
where A is the length of the vector, and θ is the angle with the x-axis. Thus:
Ax = 8 cos 71°.
To find Ax, we perform the following calculation:
- Ax = 8 × cos(71°)
- Ax ≈ 8 × 0.325568 (using a calculator)
- Ax ≈ 2.60454
Therefore, the x-component is approximately 2.6 units, which corresponds to answer option A.