One of the rectangular components of a force of 40 N is `20 sqrt(3) N.` What is the other rectangular component ?

Options

A. 10 N
B. 20 N
C. 30 N
D. 25 N

Answer

B

Explanation

The rectangular components of the force F are `F cos theta and F sin theta`, as shown in the figure.
Suppose that `F cos theta = 20 sqrt(3) N`
`therefore 40 xx cos theta = 20 sqrt(3) N`
`therefore cos theta =(20 xx sqrt(3))/(40) =(sqrt(3))/(2) therefore theta =30^(@)`
`therefore` The other component will be `F sin theta =40xx sin 30^(@) =40xx(1)/(2) =20 N`