Alpha (face-inclination angle)
57.99deg
Angle between each triangular face and the base (slant height inclination)
Beta (edge-inclination angle)48.53deg
Gamma (face base angle)57.99deg
Delta (apex angle)64.01deg
Slant height (MO)9.434m
Lateral edge (BO)10.677m
Base apothem (CM)5m
▸Square pyramid: alpha = 57.99 deg, beta = 48.53 deg
- The face-inclination angle (alpha = 57.99 deg) describes how steeply the triangular faces rise from the base.
- The lateral edge angle (beta = 48.53 deg) is always smaller than alpha because lateral edges run corner-to-apex, farther from the center than the slant height.
- Each triangular face has a base angle of 57.99 deg and an apex angle of 64.01 deg. The three angles of each triangle sum to 180 deg.
- For a square pyramid, the base apothem equals half the side length, making it easy to verify: CM = a / 2 = 5.00.
Next stepTo reverse-solve, use the alpha angle and base side length: h = CM * tan(alpha). If you want equal lateral-edge and face angles (equilateral faces), set the base side equal to the slant height.