Question

If Ax=10√3N and Ay=10N find A for resultant. Also find the angle formed the resultant with x-axis​

Answer 1

Answer -

Ax = 10√3

Ay = 10

$\bf Resultant = \sqrt{Ax^2 + Ay^2}$

$\sf Resultant \:vector = \sqrt{(10√3)^2 + (10)^3}$

$\sf Resultant \:vector = \sqrt{300 + 100}$

$\sf Resultant \:vector = \sqrt{400}$

$\bf Resultant \:vector = 20$

To find angle with x axis -

The cosines of the angles a vector makes with the cartesian coordinate axes are the direction cosines.

If vector A makes an angle

θ with the x -axis, then it's direction cosine along x- axis is, cosθ = α

Answer 2

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Everyone has given the “sin = opp/hyp” answer (aside from Victor Avasi who suggests scale drawings - a great idea!) Anyway, I thought I’d offer a different way of thinking about it. When decomposing a vector , we always have that one of the legs is and one is . Note that I’m avoiding using subscripts x & y here because the legs needn’t be parallel to the x & y axes - you are welcome to decompose a vector into any coordinate system.