Question

multiple choice question
after the magnitude of the resultant vector for the addition of two perpendicular vectors is found using the pythagorean theorem, the direction still needs to be found. the angle between vector a and the resultant vector in the diagram requires which trigonometric ratio?
o the cosecant ratio
the cosine ratio
the tangent ratio
the sine ratio

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle (formed by vectors \(A\), \(B\), and \(R\)), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\csc\theta=\frac{\text{hypotenuse}}{\text{opposite}}\).

Step2: Identify sides for the angle between \(A\) and \(R\)

Let the angle between \(A\) and \(R\) be \(\theta\). The side opposite to \(\theta\) is \(B\), and the side adjacent to \(\theta\) is \(A\).

Step3: Calculate the trigonometric ratio

\(\tan\theta=\frac{B}{A}\) (using the formula \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\))

Answer:

the tangent ratio