Question

В правильном четырехугольной пирамиде боковое ребро равно 10√3 см и наклонено к плоскости основания под углом 30° найдите сторону основания пирамиды

Answer 1

Вот решение глянь, может быть есть ошибка в вычислениях.

Answer 2

Calculation of the Base Side of the Pyramid

To find the side length of the base of the pyramid, we can use trigonometry and the given information about the slant height and the angle between the slant height and the base.

Let's denote the side length of the base of the pyramid as x.

From the given information, we know that the slant height of the pyramid is equal to 10√3 cm and it is inclined to the base at an angle of 30°.

Using trigonometry, we can relate the slant height, the side length of the base, and the angle between them.

The relationship can be expressed as:

sin(30°) = (x/2) / (10√3)

Simplifying the equation:

1/2 = (x/2) / (10√3)

Cross-multiplying:

x/2 = (1/2) * (10√3)

Simplifying further:

x/2 = 5√3

Multiplying both sides by 2:

x = 10√3

Therefore, the side length of the base of the pyramid is 10√3 cm.

Note: The calculations were performed using trigonometry and the given information.