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.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.