In a regular hexagonal pyramid, the side edge is 17 and the side of the base is 8. Find the height of the pyramid.

At the base of a regular hexagonal pyramid is a regular hexagon.
A regular hexagon consists of six equilateral triangles with angles of 60º.
Let C be the top of the pyramid, O is the center of the base, CA is one of the edges of the prism and equals 17 cm by condition.
Consider a right-angled triangle COA, CO is the height of the pyramid.
Since the hexagon consists of equilateral triangles, AO is equal to the side of the base of the pyramid, that is, AO = 8 cm.
Then the CO height is equal to:
CO ^ 2 = CA ^ 2 – AO ^ 2 = 17 ^ 2 – 8 ^ 2 = 289 – 64 = 225 cm ^ 2.
CO = 15 cm.
The height of the pyramid is 15 cm.