two forces F1 and F2 acting on an object find the resultant force on the object and direction of the resultant force F1=60N and F2= 90n?

You are looking for R = F1 + F2 in vectors; so convert these into XX YY components.

Rx = F1x + F2x = F1 cos(60) + F2 cos(30)
Ry = F1 sin(60) + F2 sin(30)

So R = sqrt(Rx^2 + Ry^2) at theta = ATAN(Ry/Rx)

R = sqrt((60 * cos(radians(60)) + 90 * cos(radians(30)))^2 + (60 * sin(radians(60)) + 90 * sin(radians(30)))^2) = 1.450968E+02 ~ 145 N at theta = ATAN(((60 * sin(radians(60)) + 90 * sin(radians(30)))/((60 * cos(radians(60)) + 90 * cos(radians(30))))) = 41.9 deg re XX axis. ANS.