How to find the height of a quadrangular pyramid if the side of the base is 8 m

How to find the height of a quadrangular pyramid if the side of the base is 8 m and the edge is inclined to the plane of the base at an angle of 60?

At the base of the pyramid lies a square with a side of 8 m. Let us construct a diagonal AC and, by the Pythagorean theorem, determine its length. AC ^ 2 = AD ^ 2 + CD ^ 2 = 64 + 64 = 128.

AC = 8 * √2 cm.

The diagonal section of the pyramid is an isosceles triangle APC AP = CP, and since, by condition, the angle PAC = 60, then the triangle APC is equilateral, AC = AP = CP = 8 * √2 cm.

Then OP is the height of an equilateral triangle. OR = AC * √3 / 2 = 8 * √2 * √3 / 2 = 4 * √6 cm.

Answer: The height of the pyramid is 4 * √6 cm.




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