Why is Work Done (Fssinθ) and Not (Fscosθ)?

Have you ever wondered why work done is usually written as (Fscos θ), just like I once did?

Initially, I plugged any formula into any question of my choice until I failed a question where I was supposed to be (Fssinθ).

I argued with my professor. I even said, "Sir, are you more intelligent than Nelkon and Parker?" It wasn't funny.

Back then, my understanding of the concept of resolving forces and interpreting questions was not profound.

I knew the formulas, but I ignored the concepts behind them and the exceptions to their application.

Although I pretended to accept my professor's explanation, I went back to study the topic until I came across practical examples. I also connected the idea to the resolution of forces.

The choice of formula depends on the direction you are resolving the force—whether vertically or horizontally.

Back then, I relied on the SOHCAHTOA mnemonic. The hypotenuse is always paired with the side you are working with. If you are resolving the force vertically, as shown in the image abov, you use (\sin\theta). If you are resolving it horizontally, you use (\cos\theta).

A common question is usually presented like this:

A boy pulls a cart with a rope inclined at an angle of 30 degrees to the horizontal. Calculate:
(a) the work done in pulling the cart, and
(b) the force raising the cart from the ground.

Now you can see that the formula you use depends on the direction of the force required in the question.

I hope that with these few points of mine, I have been able to convince you and not confuse you.

Bye!!!!

Thanks to @ecency and @stemsocial for their supports.
Image was created using Chatgtp.