Question

Ветер сломал дерево, высота которого была 24 м. Вершина этого дерева упирается в землю. На какой высоте переломилось дерево, если отломанная часть с поверхностью земли образует угол в 30 градусов?

Answer 1

Ответ:

8м

Пошаговое объяснение:

После падения дерево образовало прямоугольный треугольник. Малый катет расположен против угла в 30° и составляет 1/2 от гипотенузы. Сумма гипотенузы и короткого катета равна 24м. Таким образом

x +2x = 24

Отсюда x = 8м

Answer 2

Ответ:

дерево переломилось на высоте 8 метров

Пошаговое объяснение:

Answer 3

Problem Analysis

We are given that a tree, with a height of 24 meters, was broken by the wind. The top of the tree is touching the ground, and the broken part forms a 30-degree angle with the surface of the ground. We need to find the height at which the tree broke.

Solution

Let's assume that the height at which the tree broke is 'x' meters from the ground. We can use trigonometry to solve this problem.

We know that the broken part of the tree forms a 30-degree angle with the surface of the ground. This forms a right triangle, with the height of the tree (24 meters) as the hypotenuse, the height at which the tree broke (x meters) as the opposite side, and the distance from the base of the tree to the point where it broke as the adjacent side.

Using the trigonometric function sine, we can write the equation:

sin(30 degrees) = opposite/hypotenuse

Substituting the known values:

sin(30 degrees) = x/24

Simplifying the equation:

x = 24 * sin(30 degrees)

Now, we can calculate the value of 'x' using this equation.

Calculation

Let's calculate the value of 'x':

x = 24 * sin(30 degrees)

Using a calculator:

x ≈ 12 meters

Therefore, the tree broke at a height of approximately 12 meters from the ground.

Answer

The tree broke at a height of approximately 12 meters from the ground.