Question

Из точки N к плоскости проведена наклонная длиной 14 см.Она образует с плоскостью угол 45 градусов.Найти длину перпедикуляра NK к плоскости.

Answer 1

Наклонную обозначим NL

NL=14 см

угол NLK=45 град

Рассмотрим треугольник NLK. Он прямоугольный, т.к. угол К=90 град.

Угол KNL=90-45=45 град

Угол KNL=углу NLK, значит треугольник NLK равнобедренный, т.е. KL=KN

Найдём длину KN по теореме Пифагора

KN^2+KL^2=14^2

2KN^2=196

KN^2=98

KN=sqr(98)   sqr-это корень квадратный

KN=7sqr(2)

Answer 2

Finding the Length of the Perpendicular NK to the Plane

To find the length of the perpendicular NK to the plane, we need to use the given information that a slant line is drawn from point N to the plane, forming a 45-degree angle with the plane. The length of the slant line is given as 14 cm.

Let's denote the length of the perpendicular NK as x.

To solve for x, we can use trigonometry. In a right triangle, the sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the angle between the slant line and the plane is 45 degrees, and the slant line is the hypotenuse of the right triangle.

Using the sine function, we can write:

sin(45 degrees) = NK / 14 cm

Since the sine of 45 degrees is equal to 1/sqrt(2), we can rewrite the equation as:

1/sqrt(2) = NK / 14 cm

To solve for NK, we can cross-multiply and simplify:

NK = 14 cm / sqrt(2)

Using a calculator, we can approximate the value of NK:

NK ≈ 9.9 cm

Therefore, the length of the perpendicular NK to the plane is approximately 9.9 cm.

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