It was online, you put two dimensions in and it works out the angles. Or put in one angle and one measurement and works out other dimensions
I would have thought you need to know at least one angle in a non right angle triangle to find the others. 47.5 seems steep, when the max pitch for domestic use is only 42 degrees. Unless as others point out you are measuring the opposite angle. I have calculated the pitch as Jord mentions using a sliding bevel aligned to stri g the use a lever to plumb bevel. This is then referenced on a rafter square.
Of the two unknown angles and three lengths in a right angle triangle you only need to know two of them to work out the rest. From the dimensions dvd has given he is correct.
For what it's worth the last 3 staircases that I had reason to measure the pitch they were all around 43deg, these ranged from Victorian terrace to 1950ish semi, just measured mine and it's 44deg.
A 20 year old house should have a max angle of 42deg (AD K) so as others have said it is likely you are looking at the wrong angle. There is an easy way to check without more maths: measure the overall depth of a single tread and deduct the nose overhang. This is the "GO". If this is greater than the height of the single step, the "RISE", then you are less than 45deg. as we suspect.
I am still not sure how he's managed to get the measurements, do you have a picture. I would say that he has got the angle from the newel post (plum) to the riser. If newel post is plum, call this 90° Then minus 47.5°from this equals 42.5°. So he could be right after all, but they are asking for the pitch, unless 'rake' means something else?? I would go and buy a angle meter just to be on the safe side.
Personally if I was having a glass stairs like that fitted I'd be taking no responsibility with measuring. The person supplying the glass would be doing the site visit and measuring and if wrong, he owns it. Not that dvd's is anything like that.
If you are cutting glass it needs to be absolutely perfect - forget a template unless it's full size of your stairs. Forget Pythagoras (although it can be worked that way). mark a spot on your baserail near the bottom of the stair. Use a laser and make a mark a point on the horizontal under the top of the stair level with that mark. Measure the distance from the mark on the base rail to that point. Set a vertical with the laser from that point so it crosses the baserail at high level. Measure the vertical distance from the point to where the laser crosses the baserail so you have a vertical distance. TAN (The angle of the stair) = Vertical height/horizontal distance. so on your calc divide vertical by horizontal then INVERSE TAN and you have your answer. You know it will be around 42 deg, and doing it this way you will get the angle to several decimal places. You NEED that accuracy. In fact, use this quick calculator - you will have an answer around 0.9 to enter into the inverse tan calculator to find the angle https://www.rapidtables.com/calc/math/Tan_Calculator.html