Question

Two forces of 545 N and 218 N act at a point. The resultant force is 619 N.find the angle between the forces

Answer 1

Answer:

90.93 degrees

Step-by-step explanation:

Let us consider the angle between two forces $\theta$.

As per the parallelogram rule we know that the sum vector is along the diagonal of the parallelogram, splitting the parallelogram into two triangle with sides of lengths 545 N, 218 N, and 619 N. The angle opposite to the side of length 619 is (π - θ) radians. Now apply the law of cosines to finish.

$619^2= (545)^2+ (218)^2 -2 \times 545 \times 218 \times (cos (\pi -\theta))$

$383161=297025+47524-237620 \times cos (\pi - \theta)$

$383161=344549-237620 \times cos (\pi - \theta)$

$38612=237620 \times cos(\pi -\theta)$

$0.0162=cos (\pi -\theta)$

$(\pi -\theta)= cos^{-1}(0.0162)$

$\pi - \theta = 89.07$

$\theta = 180^\circ - 89.07^\circ$

$\theta = 90.93$

Therefore, the angle between two forces is 90.93 degrees.