Question

Реши задачу и запиши ответ Дан прямоугольный параллелепипед, в основании которого лежит квадрат со стороной равной 13 см. Диагональ пареллелепипеда наклонена к плоскости основания под углом 60°. Найди боковое ребро параллелепипеда. Ответ:​

Answer 1

Приветик, ответ на фото<3

Answer 2

Problem Analysis

We are given a rectangular parallelepiped with a square base of side length 13 cm. The diagonal of the parallelepiped is inclined to the plane of the base at an angle of 60°. We need to find the length of one of the lateral edges of the parallelepiped.

Solution

To solve this problem, we can use trigonometry and the properties of right triangles.

Let's denote the side length of the square base as s (s = 13 cm) and the length of the lateral edge of the parallelepiped as x.

We can start by finding the length of the diagonal of the square base. The diagonal of a square can be found using the Pythagorean theorem. The diagonal of the square base is equal to the hypotenuse of a right triangle with the sides equal to the side length of the square.

Using the Pythagorean theorem, we have:

diagonal of the square base = √(s^2 + s^2) = √(2s^2) = s√2

Now, let's consider the right triangle formed by the diagonal of the parallelepiped, one of the lateral edges, and the diagonal of the square base. The angle between the diagonal of the parallelepiped and the plane of the base is 60°.

Using trigonometry, we can relate the length of the diagonal of the parallelepiped, the length of the lateral edge, and the length of the diagonal of the square base.

In a right triangle, the sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is the length of the lateral edge, and the hypotenuse is the length of the diagonal of the parallelepiped.

We have:

sin(60°) = x / (s√2)

Simplifying this equation, we get:

x = (s√2) * sin(60°)

Now, let's substitute the given values into the equation and calculate the length of the lateral edge.

x = (13 cm * √2) * sin(60°)

Using a calculator, we can find:

x ≈ 22.63 cm

Therefore, the length of one of the lateral edges of the parallelepiped is approximately 22.63 cm.

Answer

The length of one of the lateral edges of the parallelepiped is approximately 22.63 cm.