Question

Помогите, пожалуйста, решить задачу и сделать чертёж. Даны две взаимно перпендикулярные плоскости и прямая, пересекающая их. Отрезок этой прямой, заключённый между плоскостями, равен 20 см. Проекции отрезка на плоскости равны 16 см и 15 см. Найдите длину проекции этого отрезка на линию пересечения плоскостей.​

Answer 1

Ответ: 9 см

Объяснение: во вложении

Answer 2

Problem Statement

You are given two mutually perpendicular planes and a line that intersects them. The segment of this line between the planes has a length of 20 cm. The projections of this segment onto the planes are 16 cm and 15 cm. You need to find the length of the projection of this segment onto the line of intersection of the planes.

Solution

To solve this problem, we can use the concept of similar triangles. Let's denote the length of the projection of the segment onto the line of intersection of the planes as x.

We can set up the following proportion based on the similar triangles formed by the given information:

x / 20 = 16 / 15

To find the value of x, we can cross-multiply and solve for x:

x = (20 * 16) / 15

Calculating this expression, we find that x ≈ 21.33 cm.

Therefore, the length of the projection of the segment onto the line of intersection of the planes is approximately 21.33 cm.

Conclusion

The length of the projection of the given segment onto the line of intersection of the planes is approximately 21.33 cm.