⇒ I expect this choice got careful consideration. (Edit: in the end, the reasoning still could have been “unfortunately, existing implementations do it this way; we’ll begrudgingly follow them”)
Indeed, and makes you realise that NaN is not "not a number" but rather "not a particular number", if one cathetus is infinite then the hypotenuse must be infinite whatever the other cathetus is ...
⇒ I expect this choice got careful consideration. (Edit: in the end, the reasoning still could have been “unfortunately, existing implementations do it this way; we’ll begrudgingly follow them”)