In a regular quadrangular pyramid, the angle between the height and the side edge is 60 degrees

In a regular quadrangular pyramid, the angle between the height and the side edge is 60 degrees, the side of the base of the pyramid is 12√2 cm. Find the length of the side edge of the pyramid.

Let us define the diagonal of the base d.
d ^ 2 = (12√2) ^ 2 + (12√2) ^ 2;
d ^ 2 = 144 * 2 + 144 * 2 = 288 + 288;
d ^ 2 = 576;
d = √578 = 24 cm.
Let’s determine the height of the pyramid h.
tg30 = h: d / 2;
h = tg30 * d / 2;
2h = tg30 * d;
2h = 1 / √3 24;
h = 12 / √3 cm.
Let’s define the edge of the pyramid b.
b = 2h;
b = 2 * 12 / √3 = 24 / √3;
b = 24: 1.73 = 13.87 cm.
Answer: the edge of the pyramid is 13.87 cm.