Galaxy tab s10 plus issue connecting to projector

Hi guys.

I recently bought the newest tablet, S10 Plus, for school (as a teacher). Our school has "Epson" projectors, but they are unfortunately a bit old, so most of them don't have an HDMI port, as does the one in my classroom.

When I used to use a laptop, I had an adapter that convert the connection from VGA (the blue one with the screws) to HDMI for my laptop, and it works perfectly. But recently when I bought the tablet, I suffered from connecting it to the projector till today.

What I use is 1- an adapter (VGA to HDMI). 2- an adapter (Type C to HDMI). it means that I use 2 types of adapters just to connect the projector to my tablet. Sadly, it doesn't show any image on the projector screen. I tried a lot of ways to solve the problem. like: checking the source of the projector, connecting my tablet to a power supply (plugging it into the charger), and changing the media output in my tablet (it was just for sound).

I really don't know if the problem was me doing something wrong, that old projector, the tablet itself, or the adapters I use. Besides, when I connect the adapters to my tablet it gives me a message (external display connected), but no image is showing on the projector. I really hope that the solution would be to buy a specific adapter...

I really need some help or advice to make this work, or it will be a waste of 1.2k dollars.