Editorial for Appleby Contest '20 P1 - Terrific Triangles

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Author: kdrkdr

Subtask 1

For the first subtask, there are only two types of triangles. Thus, it suffices to only check if the triangle is a right angle using the Pythagorean Theorem. If not, the triangle can only be obtuse.

Subtask 2

Notice that if the triangle is acute, $a^2+b^2 > c^2$ $a^{2} + b^{2} > c^{2}$ for hypotenuse $c$ $c$ and side $a$ $a$ , $b$ $b$ ; if the triangle is obtuse, $a^2+b^2 < c^2$ $a^{2} + b^{2} < c^{2}$ .

The intuition comes from fixing the length of the two shorter sides. Starting from a right triangle, if the angle between $a$ $a$ and $b$ $b$ decreases, the length hypotenuse also decreases, and vice versa.

Using this fact, we can simply solve for the type of triangle by testing it against the aforementioned inequalities.

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