I have a question that i am struggling to come to terms with. I know how to get the answer but i am not 100% sure why what i am doing works.(adsbygoogle = window.adsbygoogle || []).push({});

The question :

A smooth plane is inclined at X degrees to the horizontal.

A block of mass 5KG is held at rest on the plane by a horizontal force of magnitude 168N.

Find :

Angle X

The force on Normal on the block.

Ok, so far i have this.

i seperated the horizontal force of 168N into a force horizontal and a force parralel to the plane.

Horizontal : 168CosX = 5gsinX

parallel : N = mgcosX + 168sin X

Now somehow, and this is the part i do not understand 100%

you get to the equation

5gcosX=168cosX

sinX/cosX=168/5g

tanX=168/5g

so then X is the tan^-1 of (168/5g).

and then you put it back in the parallel equation to find N, the normal.

Can someone explain to me how you come about reaching these equations :

5gcosX=168cosX

sinX/cosX=168/5g

tanX=168/5g

thank you.

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