Question

A vector has an x-component of length 3.5 and a y-component of length 3. What is the angle of the vector? (Hint: Use the inverse tangent.)

A. 59.0°
B. 40.6°
C. 31.0°
D. 67.2°

Answer 1

`B. 40.6\degree`

Step-by-step explanation

A sketch of the vector is shown in the diagram in the attachment.

The side adjacent to the angle we want to find is 3.5 units and the opposite side is 3 units.

Let the angle between the vector and the x-axis be
`\phi`

then,

`\tan\phi =(3)/(3.5)`

`\tan\phi=0.8571`

This implies that,

`\phi=tan{-1}(0.8571)`

`\phi=40.6013`

The correct answer is B

Therefore the angle 40.6° to the nearest tenth.