Final answer:
The triangle described is a right-angled triangle, as indicated by references to trigonometric functions and the Pythagorean theorem.
Step-by-step explanation:
The type of triangle described can be identified by understanding certain key concepts. First, since there is a reference to the sine, cosine, and tangent of angles, and these are defined for right-angled triangles, the triangle in question here is most likely a right-angled triangle. In addition, the mention of the Pythagorean theorem, which relates the sides of a right triangle, confirms this. Finally, the description of an angle being either equatorial (in the plane) or axial (above or below the plane the triangle) fits the context of a trigonal bipyramidal shape rather than a triangle, which might appear in a chemistry context.