Question

Отрезок АВ перпендикулярен к плоскости а . Наклонная АС образует с плоскостью а угол 60 , а наклонная АД равна 7 см . Длинна проекции наклонной ВД равна 2 см . Вычислите длину наклонной АС и рисунок

Answer 1

Ответ:

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Объяснение:

Answer 2

Problem Analysis

We are given the following information: - Line segment AB is perpendicular to plane a. - Inclined line AC forms a 60-degree angle with plane a. - Inclined line AD has a length of 7 cm. - The length of the projection of inclined line BD is 2 cm.

We need to find the length of inclined line AC.

Solution

To solve this problem, we can use the concept of right triangles and trigonometry.

Let's consider triangle ABD. Since AB is perpendicular to plane a, we can consider it as the base of a right triangle. The inclined line AD is the hypotenuse, and the projection of BD is the height of the triangle.

Using the Pythagorean theorem, we can find the length of BD: BD^2 = AD^2 - AB^2 BD^2 = 7^2 - 2^2 BD^2 = 49 - 4 BD^2 = 45 BD = √45 cm

Now, let's consider triangle ABC. We know that angle BAC is 60 degrees. Since AB is perpendicular to plane a, we can consider it as the base of a right triangle. The inclined line AC is the hypotenuse, and the projection of BD is the height of the triangle.

Using trigonometry, we can find the length of AC: sin(60) = BD / AC sin(60) = √45 / AC AC = √45 / sin(60)

Now, let's calculate the value of AC.

Calculation

Using the given information and the formulas derived above, we can calculate the length of AC.

BD = √45 cm AC = √45 / sin(60) cm

Using a calculator, we can find the value of sin(60) to be approximately 0.866.

AC = √45 / 0.866 cm AC ≈ 7.745 cm

Therefore, the length of inclined line AC is approximately 7.745 cm.

Diagram

Unfortunately, I am unable to provide a diagram in this text-based format. However, you can visualize the problem by considering a right triangle ABC, where AB is the base, AC is the hypotenuse, and BD is the height. Angle BAC is 60 degrees, and the length of BD is 2 cm.

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