Answer:
The angle between vectors A and B is 116.6°.
Explanation:
Geometric Addition of Vectors
The geometric construction of the situation stated in the question is shown in the image below.
The angle between vectors A and B is the sum of 90° and θ.
Angle θ can be found by working on the right triangle of side lengths 8 and 4, and angle θ.
We use the tangent ratio:
[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
The opposite leg to θ is 4 and the adjacent leg is 8, thus:
[tex]\displaystyle \tan\theta=\frac{4}{8}=\frac{1}{2}[/tex]
Calculating the angle:
[tex]\displaystyle \theta=\arctan\left(\frac{1}{2}\right)[/tex]
[tex]\theta\approx 26.6^\circ[/tex]
Thus the required angle is 90° + 26.6° = 116.6°
The angle between vectors A and B is 116.6°.
