Question

A plane bisects a 90degree dihedral angle. From a point on this plane 16 in. from the common edge, perpendicular lines are constructed to the respective faces of the dihedral angle. Find the length of each perpendicular.

Answer 1

If we cut the dihedral with a plane perpendicular to the edge we obtain a 90 degrees angle cut by its bisecting line.
As far as this problem is concerned, the distances from the points of the planes are the same as the distances from the points of the lines in the normal section.
All the points of the bisecting line are equidistant from the sides, and the perpendiculars to the sides form two congruent right isosceles triangles.
Then if a point on the line is 16 in from the vertex, its distance from the sides is
16 / √2 = 8√2 = 11.3 inches