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How do I refer to each vertex of a right triangle by its angle property. I know the common angle classifications: acute, right, obtuse, straight and reflex. But what about a right scalene triangle, which has one angle $<45^\mathrm{o}$ and another between $45^\mathrm{o}$ and $90^\mathrm{o}$? I would like to have names for these angle types also.

I could refer to these verbosely, as "the vertex at the short (or long) edge of the triangle", but would prefer to use a vertex name. Though quite polysyllabic, I thought perhaps semi-acute and semi-obtuse (two semi-right angles for a right isosceles) but found no previous use of such terms. How would you distinguish these vertices?

For context, I am working with two pyramids which have a right scalene triangle base in common, and a peak that is orthogonal to an acute corner of the base. I wish to refer to each pyramid according to whether the peak is above the $<45^\mathrm{o}$ or $>45^\mathrm{o}$ base vertex.

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  • $\begingroup$ You could call them the smaller/larger (acute) angles, or the vertices opposite the smaller/larger legs of the right triangle. $\endgroup$
    – dxiv
    Jul 16, 2022 at 5:40
  • $\begingroup$ I'd give those vertices two labels, e.g. $A$ and $B$. $\endgroup$
    – Intelligenti pauca
    Jul 16, 2022 at 9:32

1 Answer 1

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Consider the humble $\space(3,4,5)\space$ triangle below. I always think of the legs $(A,B)$ of a Pythagorean triple as positive $(x,y)$ coordinates respectively. I also think of the angles as being adjacent and opposite, corresponding to the legs they are connected to. So, below, the $\space53˚\space$ angle is the adjacent and the $\space37˚\space$ angle is the opposite. This may not be a math standard but it is a convenient convention. enter image description here

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