In a regular quadrangular pyramid, the side is 2 cm, and the height is 6 cm.
| June 19, 2021 | education
In a regular quadrangular pyramid, the side is 2 cm, and the height is 6 cm. Find the angle of inclination of the side edges to the plane of the base.
At the base of a regular pyramid is a square, then AB = BC = CD = AD = 2 cm.
Let’s draw the diagonals AC and BD and determine their length.
AC ^ 2 = AD ^ 2 + CD ^ 2 = 4 + 4 = 8.
AC = √8 = 2 * √2 cm.
Since the diagonals at the intersection point are divided in half, then AO = CO = AC / 2 = 2 * √2 / 2 = √2 cm.
The MOC triangle is rectangular, then tgMCO = MO / CO = 6 / √2 = 6 * √2 / 2 = 3 * √2.
Angle MCO = arctan (3 * √2).
Answer: The angle between the side edge and the plane of the base is arctan (3 * √2).
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