Question

З точки до площини проведено дві похилі.Одна з похилих дорівнює 10 см і має проекцію завдовжки 8 см.Знайдіть довжину другої похилої , якщо вона утворює з даною площиною кут 30градусів. Помогите пожалуйста(((

Answer 1

Ответ:12 см.

Пошаговое объяснение:

Answer 2

#### Problem Analysis We are given that two inclined lines are drawn from a point to a plane. One of the inclined lines has a length of 10 cm and a projection of 8 cm. We need to find the length of the second inclined line, which forms an angle of 30 degrees with the given plane. #### Solution Let's denote the length of the second inclined line as **x**. To solve this problem, we can use trigonometry. Specifically, we can use the sine function to relate the angle and the lengths of the sides of a right triangle. In the given problem, we have a right triangle formed by the second inclined line, its projection on the plane, and the line perpendicular to the plane. The angle between the second inclined line and the plane is 30 degrees. Using the sine function, we can write the following equation: **sin(30 degrees) = (projection of the second inclined line) / (length of the second inclined line)** We know that the projection of the second inclined line is 8 cm, so we can substitute this value into the equation: **sin(30 degrees) = 8 cm / x** To find the value of **x**, we can rearrange the equation: **x = 8 cm / sin(30 degrees)** Now, we can calculate the value of **x** using the given equation: **x = 8 cm / sin(30 degrees)** Using a calculator, we can find that **sin(30 degrees) = 0.5**. Substituting this value into the equation, we get: **x = 8 cm / 0.5 = 16 cm** Therefore, the length of the second inclined line is **16 cm**. #### Answer The length of the second inclined line is **16 cm**.