Why do we use Newtons of force over trig functions?

[IBdoomed]

The problem is as follows: A mass is held by two cables attached to a wall and ceiling. The mass M is 5 kg and the angle between the string and the vertical is θ= 25°

a) Determine the tension in the cable attached to the ceiling.

I know that the answer is 55 N (because she posted the teacher posted the answers), and i know that the answer was derived by using the equation Ft= 50N/ Cos(25)

My question is why does the equation look like this when in other problems the answer comes from "magnitude of vector * desired trig function(θ)"

Bottom line: what key information tell me to put the Newtons of force over the trig function?


PLEASE LEMME KNOW ASAP CUZ THE TEST IS TOMORROW!

 

[PeterO]

The problem is as follows: A mass is held by two cables attached to a wall and ceiling. The mass M is 5 kg and the angle between the string and the vertical is θ= 25°

a) Determine the tension in the cable attached to the ceiling.

I know that the answer is 55 N (because she posted the teacher posted the answers), and i know that the answer was derived by using the equation Ft= 50N/ Cos(25)

My question is why does the equation look like this when in other problems the answer comes from "magnitude of vector * desired trig function(θ)"

Bottom line: what key information tell me to put the Newtons of force over the trig function?


PLEASE LEMME KNOW ASAP CUZ THE TEST IS TOMORROW!

In this case you know the vertical component has to balance the weight of the mass. In the problems you are alluding, we know the tension in the string and are trying to find the components.

Take the trig expression.

Cosθ = Adj / hypot.

If you want to calculate the adjacent side this re-arranges to Adj = hypt * cosθ

If you want the hypotenuse, this re-arranges to hypot = adj / cosθ

similar arrangements with sin ad tan.