Answer:
The angle between two forces is 165 degrees.
Explanation:
We have,
Force 1, [tex]F_1=27\ N[/tex]
Force 2, [tex]F_2=30\ N[/tex]
Resultant of two forces, F = 8 N
It is required to find the angle between two forces. The resultant of two force is given by the formula as follows :
[tex]F=\sqrt{F_1^2+F_2^2+2F_1F_2\cos\theta}[/tex]
[tex]\theta[/tex] is the angle between F₁ and F₂
So,
[tex]F^2=F_1^2+F_2^2+2F_1F_2\cos\theta\\\\\cos\theta=\dfrac{F^2-F_1^2-F_2^2}{2F_1F_2}\\\\\cos\theta=\dfrac{(8)^2-(27)^2-(30)^2}{2\times 27\times 30}\\\\\cos\theta=-0.966\\\\\theta=\cos^{-1}\left(-0.966\right)=165^{\circ}[/tex]
So, the angle between two forces is 165 degrees.
