Question

Концы отрезка лежат в двух взаимно перпендекулярных плоскостях. Проекции отрезка на каждую из плоскостей соответственно равны корень из 369 (см) и 20 (см). Росстояние между основаниями перпендекуляров, проведенных из концов отрезка до плоскостей, равно 12 (см). Найти длину данного отрезка.--------------Желательно с рисунком, но самое гланое рещите поскорее

Answer 1

сделаем построение  по условию

плоскости  -бетта -альфа - перпендикулярны

отрезок АВ

проекции  

АВ1 =20 (см).

ВА1 = √369 (см)

 Росстояние между основаниями перпендекуляров,

А1В1 =12 (см).

∆АА1В1 - прямоугольный

по теореме Пифагора  

AA1^2 =AB1^2 - A1B1^2 =20^2-12^2=256

AA1 =16 см

∆АА1В - прямоугольный

AB^2 = AA1^2 +BA1^2 =16^2 +(√369)^2 =625

AB=25 см

ответ  AB=25 см

Answer 2

Problem Analysis

We are given that the ends of a segment lie in two mutually perpendicular planes. The projections of the segment on each of the planes are given as the square root of 369 cm and 20 cm, respectively. The distance between the bases of the perpendiculars drawn from the ends of the segment to the planes is 12 cm. We need to find the length of the segment.

Solution

Let's denote the length of the segment as x cm.

From the given information, we can form a right-angled triangle with the segment as the hypotenuse, one side as the projection on one plane (square root of 369 cm), and the other side as the projection on the other plane (20 cm).

Using the Pythagorean theorem, we can write the equation:

x^2 = (sqrt(369))^2 + 20^2

Simplifying the equation:

x^2 = 369 + 400

x^2 = 769

Taking the square root of both sides:

x = sqrt(769)

Therefore, the length of the segment is sqrt(769) cm.

Calculation

Let's calculate the length of the segment.

x = sqrt(769) ≈ 27.75 cm

So, the length of the segment is approximately 27.75 cm.

Diagram

Unfortunately, I am unable to provide a diagram in this text-based format. However, you can visualize the problem by considering two perpendicular planes intersecting at a right angle. The segment connects two points in these planes, and the projections of the segment on each plane are given. The distance between the bases of the perpendiculars drawn from the ends of the segment to the planes is also given.