The side edge of a regular quadrangular pyramid is 10 m, it is inclined to the plane at an angle of 30 degrees.

| August 5, 2021 | education

The side edge of a regular quadrangular pyramid is 10 m, it is inclined to the plane at an angle of 30 degrees. Calculate the length: a) The heights of the pyramid b) the sides of the base of the pyramid

In a right-angled triangle MOB, the MO leg lies opposite the angle 30, then its length is equal to half the length of the BM hypotenuse. MO = BM / 2 = 10/2 = 5 cm.

Determine the length of the leg OB by the Pythagorean theorem. ОВ ^ 2 = BM ^ 2 – MO ^ 2 = 100 – 25 = 75.

ОВ = √75 = 5 * √3 cm.

Since there is a square at the base of the pyramid, its diagonals are equal and at the point of intersection they are divided in half, then the BOC triangle is rectangular and equilateral.

CB ^ 2 = OB ^ 2 + OS ^ 2 = 75 + 75 = 150.

CВ = √150 = 5 * √6 cm.

Answer: The height of the pyramid is 5 cm, the side of the base is 5 * √6 cm.



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