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°

Respuesta :

ANSWER


[tex]B. 40.6\degree[/tex]



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 [tex]\phi[/tex]


then,


[tex]\tan\phi =\frac{3}{3.5}[/tex]



[tex]\tan\phi=0.8571[/tex]



This implies that,



[tex]\phi=tan{-1}(0.8571)[/tex]




[tex]\phi=40.6013[/tex]


The correct answer is B


Therefore the angle 40.6° to the nearest tenth.

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