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? the cosine ratio the tangent ratio the sine ratio the cosecant ratio

Explanation:

Step1: Recall trigonometric ratios

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

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

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

Step3: Calculate the trigonometric ratio

\(\tan\theta = \frac{B}{A}\) (since \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\))

Answer:

the tangent ratio