Question

If the x-component of a vector is 17, and the angle between the vector and the x-axis is 46 degrees, what is the magnitude of the vector? Round your answer to the nearest hundredth.

Answer 1

24.47

Step-by-step explanation:

cosθ = adjacent/hypotenuse = x-component/vector magnitude, so cos46° = 17/ vector magnitude. the vector magnitude is, therefore, 24.47

FROM CK-12

Answer 2

17.00 N

Step-by-step explanation:

Given that the x-component of a vector is 17, and the angle between the vector and the x-axis is 46 degrees

The magnitude of the vector will be calculated by first resolving the vector into x component and y component.

X - component

17cos46 = 11.809

Y component

17sin46 = 12.229

We will find the resultant vector by using pythagorean theorem

R = sqrt ( X^2 + Y^2 )

R = sqrt ( 11.809^2 + 12.229^2 )

R = sqrt ( 288.995 )

R = 16.999

R = 17.00 N

Therefore, the magnitude of the vector is 17 .00N