Question

Найти длину перпендикуляра и длину проекции наклонной, если длина наклонной 5см и она наклонна в плоскости под углом 30*. ( с рисунком) Пожалуйста помогите с задачкой.

Answer 1

АВ и АС - наклонные, ОВ=8 см(проекция АВ на плоскость альфа), АВ = 10 см, Проведем с пункта А перпендикуляр к плоскости, пункт пересечения обозначим О.Треугольник АВО - прямоугольный( АО - перпендикуляр)Найдем АО по теореме Пифагора:АО^2 = 10^2 - 8^2AO^2 = 36AO = 6Треугольник САО - прямоугольный( АО - перпендикуляр)СА = 2АО = 2*6=12 см( гипотенуза в два раза больше катета, которай лежит напротив угла в 30 градусов)Ответ: 12 см

Answer 2

Finding the Length of the Perpendicular and the Length of the Projection

To find the length of the perpendicular and the length of the projection of a sloping line, we need to know the length of the sloping line and the angle at which it is inclined in the plane.

Let's assume that the length of the sloping line is 5 cm and it is inclined at an angle of 30 degrees in the plane.

To find the length of the perpendicular, we can use trigonometry. The length of the perpendicular can be calculated using the formula:

Length of the perpendicular = Length of the sloping line * sin(angle)

Substituting the given values, we have:

Length of the perpendicular = 5 cm * sin(30 degrees)

To find the length of the projection, we can use the formula:

Length of the projection = Length of the sloping line * cos(angle)

Substituting the given values, we have:

Length of the projection = 5 cm * cos(30 degrees)

Now, let's calculate the values using these formulas.

Using a scientific calculator or trigonometric tables, we find that:

sin(30 degrees) = 0.5 cos(30 degrees) = 0.866

Substituting these values into the formulas, we get:

Length of the perpendicular = 5 cm * 0.5 = 2.5 cm Length of the projection = 5 cm * 0.866 = 4.33 cm

Therefore, the length of the perpendicular is 2.5 cm and the length of the projection is 4.33 cm.

Please note that the values provided are based on the assumption that the length of the sloping line is 5 cm and it is inclined at an angle of 30 degrees in the plane. If the values are different, the calculations will vary accordingly.

I hope this helps! Let me know if you have any further questions.