Two for are at an angle at 120 ,the bigger forces is 40N and the resultant is perpendicular to the smaller one. find the smaller force

smaller force is 20

Explanation:

Let, magnitude of the smaller force be F Newton.

Now, the resultant force makes an angle 90° with the smaller force. So, angle between resultant force and the larger force = (120° - 90°) = 30°.

So, tan 30° = (F * sin 120°) / (40 + F * cos 120°)

(1 / √3) = {F * (√3) / 2} / {40 + F * (- 1 / 2)}

80 - F = 3F

4F = 80

F = 20.

So, magnitude of smaller force is 20 Newtons.

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