Rational Trigonometry vs Regular Trigonometry

Professor NJ Wildberger stated that Rational Trigonometry is the "correct" way to teach Trigonometry. I saw one of his video lessons. I disagree. You say?

 

An essential point of his "rational trigonometry" is that quadrance and spread, not distance and angle, are the right concepts for metrical geometry.
Quadrance measures the separation of points, and spread measures the separation of lines.

In my opinion of a Math "without Reals" is the same as English without vowels.

It appears to me that Wildberger is "re-discovering "some ideas from constructive mathematics and is relating them to the teaching of mathematics. Not only is there a link to Brouwer's intuitionism, but Wildberger's worries about infinite sets also appear to be related to the finitism of Leopold Kronecker.

I don't understand are his rather bizarre views on a few mathematical concepts that I thought were generally accepted as true: non-existence of infinite sets, the Real Numbers, and transcendental functions.

The simplest way to explain this is in terms of the his quote, "New laws now replace the Cosine law, the Sine law, and the dozens of other trigonometric formulas."
So solving trigonometric problems is done in essentially the same way as before. Gather the known values, construct the relevant triangles, apply the (memorized) laws to create relevant equations, and solve the equations algebraically for the desired values (using a calculator to evaluate complex functions).
Only now you use the new laws instead of old ones. As far as I can tell, the trigonometric TECHNIQUES have not changed. He claims the advantage that a calculator is generally no longer needed because he doesn't use sine, cosine, tangent, etc., but he hasn't escaped the square root, so I don't consider that claim valid.

 

He has a weird way of teaching math but intelligent nonetheless.