MathDB

Regular Tetrahedron

Source: 1998 National High School Mathematics League, Exam One, Problem 5

March 9, 2020

geometry3D geometrytetrahedron

Problem Statement

In regular tetrahedron

ABCD

E,F,G

are midpoints of

AB,BC,CD

. Dihedral angle

C-FG-E

is equal to

\text{(A)}\arcsin\frac{\sqrt6}{3}\qquad\text{(B)}\frac{\pi}{2}+\arccos\frac{\sqrt3}{3}\qquad\text{(C)}\frac{\pi}{2}-\arctan{\sqrt2}\qquad\text{(D)}\pi-\text{arccot}\frac{\sqrt2}{2}