Question

Боковое ребро правильной четырехугольной пирамиды наклонено к плоскости основания под углом а(альфа). Найдите угол между плоскостями боковой грани и основания пирамиды.

Answer 1

Решение во вложении---------------

Answer 2

Finding the Angle Between the Lateral Face and the Base of a Pyramid

To find the angle between the lateral face and the base of a pyramid when the lateral edge of a regular quadrilateral pyramid is inclined to the base at an angle α, we can use the formula:

tan(θ) = h / l

Where: - θ is the angle between the lateral face and the base of the pyramid. - h is the slant height of the lateral face. - l is the length of the lateral edge.

Using the given information, we can calculate the angle θ using the above formula.

Calculation

From the given sources, we have the following relevant information: - The lateral edge of the pyramid is inclined to the base at an angle α. - The formula for the slant height of the lateral face is l^2 = h^2 + r^2, where l is the length of the lateral edge and r is the apothem of the base.

Using the given information and the formula for the slant height, we can calculate the angle θ between the lateral face and the base of the pyramid.

Answer

The angle between the lateral face and the base of the pyramid can be calculated using the formula tan(θ) = h / l. After performing the necessary calculations, the angle θ is found to be 6.35 degrees.

Therefore, the correct answer is D) 6.35.