Track / Stage 4 / 294 of 340 #554 of 2000

167. Prove that if all plane angles of a trihedral angle are obtuse, then all dihedral angles are also obtuse.

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

I solved it I didn't Skip

Official solution

167. Use the first cosine theorem (see problem 166).

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.