find magnitude of two forces such that if they Act at right angle their resultant is 90N and when they Act at 60 degree their resultant is 117N
Hi Dipak, hope you are doing well,
Let the forces be F1 and F2
F1^2 + F2^2 = 90 N
(as the angle between them is 90° or right angle)
when angle is 60°
F1^2 + F2^2 + 2 * F1 * F2 *cos(60)=117 N
90 + F1 * F2=117
F1 * F2 = 27
(F1 + F2)^2 = F1^2 + F2^2 + 2 * F1 * F2 = 90+27×2=144
F1 + F2 = 12..............(i)
F1 - F2 = √( ( F1 + F2)^2 - 4F1 * F2) = √36 = 6.........(ii)
from eq.(i) and (ii) We get....
F1 = 9 N ,and F2 = 3 N
Feel free to ask doubts in the Comment Section like this.
I hope this helps you.