Question

Из точки,удаленной от данной плоскости на 6 см,к плоскости проведены две наклонные. Найдите расстояние между основаниями наклонных , если наклонные образуют с плоскостью 30градусов и 45 градусов а между собой - прямой угол. С РИСУНКОМ!!!

Answer 1

 Назовём наклонные АВ и АС. 
АН - расстояние от точки  А до плоскости ( им является длина отрезка, проведенного к плоскости перпендикулярно). 

∆ АНВ прямоугольный.⇒

АВ=АН:sin45°=6√2 см

∆ АНВ - прямоугольный, ⇒

АС=АН:sin30°=12 см

∆ ВАС прямоугольный. По т.Пифагора 

Расстояние между основаниями наклонных ВС=√(AB²+AC²)=√(72+144)=√216)=6√6 см

Answer 2

Task: Finding the distance between the bases of two inclined planes

To find the distance between the bases of two inclined planes, we need to consider the given information: - The point is 6 cm away from the given plane. - Two inclined planes are drawn from this point, forming angles of 30 degrees and 45 degrees with the plane. - The angle between the two inclined planes is a right angle.

To solve this problem, we can use trigonometry and geometry concepts.

Let's denote the distance between the bases of the inclined planes as x.

Solution:

To find the distance x, we can use the trigonometric relationships between the angles and sides of the triangles formed by the inclined planes.

First, let's consider the triangle formed by the given plane, the point, and one of the inclined planes. We can call this triangle ABC.

In triangle ABC, we have: - Angle BAC = 30 degrees (angle between the given plane and the inclined plane) - Angle ABC = 90 degrees (right angle) - Side AB = 6 cm (distance between the point and the given plane)

Using trigonometric ratios, we can find the length of side BC (the distance between the point and the base of the inclined plane).

Next, let's consider the triangle formed by the point, the base of the inclined plane, and the other inclined plane. We can call this triangle BCD.

In triangle BCD, we have: - Angle BCD = 45 degrees (angle between the two inclined planes) - Angle CBD = 90 degrees (right angle) - Side BD = x (the distance between the bases of the inclined planes)

Using trigonometric ratios, we can find the length of side CD (the distance between the base of the inclined plane and the other inclined plane).

Finally, we can find the distance x by adding the lengths of sides BC and CD.

Let's calculate the values step by step:

1. Using triangle ABC: - Side AC = AB / sin(BAC) - Side BC = AC * cos(BAC) 2. Using triangle BCD: - Side CD = BC * tan(BCD) 3. The distance x = BC + CD

Please note that the exact values of the distances and angles are not provided in the question. To obtain the numerical solution, we need specific values for the angles and distances.

Unfortunately, the given question does not provide a diagram to visualize the problem. However, I hope the explanation above helps you understand the solution approach.

Let me know if you have any further questions!