Question

Two forces of 401 newtons and 477 newtons act on a point. The resultant force is 828 newtons. Find the

angle between the two forces.

The angle between the two forces is ____°

(Round to the nearest integer as needed.)

Answer 1

The answer is "
`39.01^(\circ)`"

Explanation:

`\to R= 828\\\\\to F_1= 401\\\\\to F_2=477\\\\\to \bold{R=√(F_1^2+F_2^2+2F_1F_2 \cos \theta)}`

`828=√(401^2+477^2+2 * 401 * 477 \cos \theta)\\\\828=√(160801+227529+382554 \cos \theta)\\\\828=√(388330+382554 \cos \theta)\\\\`

square the above equation:

`(828)^2=(√(388330+382554 \cos \theta))^2\\\\`

`685584 =388330+382554 \cos \theta\\\\685584 -388330=382554 \cos \theta\\\\297254=382554 \cos \theta\\\\\cos \theta=(297254)/(382554)\\\\\cos \theta=0.777025\\\\\theta= \cos^(-1) 0.777025\\\\\theta= 39.01^(\circ)`