Dihedral angle between face and base

Statement

Calculate the dihedral angle between a lateral face and the base of a right pyramid with a square base of side $4$ and height $3$.

Solution

The normal section of the face-base dihedral angle is obtained in the right triangle whose legs are the height $h$ of the pyramid and the apothem of the base $m$. Here the apothem of the base is half the side: $m = 2$. $\tan\alpha = \frac{h}{m} = \frac{3}{2}.$ Hence $\alpha = \arctan\!\left(\tfrac{3}{2}\right) \approx \boxed{56{,}3°}.$

Links

Topics: Synthetic geometry in space
Concepts: Dihedral angle · Pyramid · Normal section
Skills: Calculating · Synthetic geometry
Exercise types: Geometric problem