Question

. find the magnitude of the two forces such that it they are at right angles, their resultant is /10 N, But if they act an 60 degree ,their resultant is /13 N

Answer 1

let the forces be f1 and f2
f1²+f2²=10
as the angle between them is 90 degrees
when angle is 60
f1²+f2²+2*f1*f2*cos(60)=13
10+f1*f2=13
3=f1*f2
(f1+f2)²=f1²+f2²+2*f1*f2=10+6=16
f1+f2=4...(1)
f1-f2=√((f1+f2)²-4f1*f2)=2...(2)
from (1) and (2) u get
f1= 3 N f2= 1 N

Answer 2

f1²+f2²=10
f1²+f2²+2*f1*f2*cos(60)=13
10+f1*f2=13
3=f1*f2
(f1+f2)²
=f1²+f2²+2*f1*f2
=10+6
=16
f1+f2=4
f1-f2=√((f1+f2)²-4f1*f2)=2
f1= 3 N
f2= 1 N