# Calculate the Smaller Force if the Bigger Force is 40N and the Resultant Force is Perpendicular to the Smaller Force. The Two Forces are Acting at an Angle of 120°

Let the smaller force be of the magnitude F Newton

90° is the angle made by the resultant force with the smaller force

The angle between the resultant force and the larger force = (120° – 90°) = 30°

$tan\;30^{\circ}=\frac{F\times sin\;120^{\circ}}{40+F\times cos\;120^{\circ}}$ $\frac{1}{\sqrt{3}}=\frac{F\times \frac{\sqrt{3}}{2}}{40+F\times \frac{-1}{2}}$

80 – F = 3F

4F = 80

F = 20N