Final answer:
The x-component of a vector with a magnitude of 12.0 m and an angle of 73.3° is found using the cosine function, resulting in an approximate value of 3.51 m.
Step-by-step explanation:
To find the x-component of a vector given the magnitude and the angle, you can use the cosine function. The question asks for the x-component of a vector with a magnitude of 12.0 m and an angle of 73.3°. We can represent the x-component of the vector as Ax = A cos θ, where A is the magnitude of the vector and θ (“theta”) is the angle it makes with the x-axis. Plugging the values provided into this formula gives us:
Ax = 12.0 m × cos(73.3°).
Using a calculator set to degrees, we find:
Ax = 12.0 m × 0.2924 (approximately),
Ax = 3.5088 m.
Thus, the x-component of the vector is approximately 3.51 m.