Question

Отрезок длиной 25 см упираеться своими концами в 2 перпендикулярные поскости. Расстояние от концов отрезка к плоскости 15 см и 16 см. Найти проекции отрезка на каждуюс плоскостей.

Answer 1

Проекции находятся по т. Пифагора:

1) $\sqrt{25^{2}-15^{2}}=\sqrt{625-225}=\sqrt{400}=20$

2) $\sqrt{25^{2}-16^{2}}=\sqrt{625-256}=\sqrt{369}=3\sqrt{41}$

Answer 2

Problem Analysis

We are given a line segment of length 25 cm that is perpendicular to two planes. The distances from the ends of the segment to the planes are 15 cm and 16 cm. We need to find the projections of the segment onto each of the planes.

Solution

To find the projections of the line segment onto each plane, we need to determine the lengths of the perpendiculars from the ends of the segment to the planes. Let's denote the length of the perpendicular from one end of the segment to one plane as x and the length of the perpendicular from the other end of the segment to the other plane as y.

Using the given information, we have the following equations: - x + y = 25 (the sum of the lengths of the perpendiculars is equal to the length of the segment) - x - y = 1 (the difference between the lengths of the perpendiculars is equal to the difference between the distances from the ends of the segment to the planes)

Solving these two equations will give us the values of x and y, which represent the lengths of the perpendiculars from the ends of the segment to the planes.

Adding the two equations, we get: 2x = 26 Simplifying, we find: x = 13

Substituting the value of x into one of the equations, we can solve for y: 13 - y = 1 Simplifying, we find: y = 12

Therefore, the lengths of the perpendiculars from the ends of the segment to the planes are 13 cm and 12 cm.

The projections of the line segment onto each plane are equal to the lengths of the perpendiculars. Therefore, the projections are 13 cm and 12 cm.

Answer

The projections of the line segment onto each of the perpendicular planes are 13 cm and 12 cm.