# In a right scalene triangle, can the other two angles be distinctly classified?

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.

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

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. 