SOLUTION: Kindly help: A 325-kg carton is sitting on a ramp, help stationary by 275kg of tension in a restraining rope. Find the ramp's angle of incline to the nearest tenth of a degree.

In any textbook in Physics, you can find a Figure showing force decomposition on the sloped ramp.



    See, for example, this link:  http://www.dummies.com/education/science/physics/calculating-the-force-needed-to-move-an-object-up-a-slope/



From the figure,  F = W*sin(A),  where

     W is the weight, F is the tension force, and "A" is the inclination angle.



In your case  W = 325 kg (in your case kilograms are not the mass units - they are the force units, instead),  F = 275 kg.


So, sin(A) =  =  = 0.846.


Then  A = arcsin(0.846) = 1.008 radians = 57.8 degrees.