The side edges of a regular quadrangular pyramid are inclined to the base plane

The side edges of a regular quadrangular pyramid are inclined to the base plane at an angle of 60 degrees. Find the height of the pyramid if its side edges are 12 cm.

The angle between the edge b and the height h = 90 – 60 = 30.
Let’s define half of the diameter d of the base of the pyramid.
d / 2 = b / 2;

d / 2 = 12: 2 = 6 cm.

3. Determine the height of the pyramid h.

h ^ 2 = b ^ 2 + (d | 2) ^ 2;

h ^ 2 = 12 ^ 2 – 6 ^ 2;

h ^ 2 = 144 – 36;

h ^ 2 = 108;

h = √108 = 6√ 3 cm.

Answer: the height of the pyramid is 6√3 cm.