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

To solve this problem, we can use trigonometry. Let's consider the broken part of the tree as a right triangle, with the height of the tree being the hypotenuse, the height at which the tree broke as the opposite side, and the distance from the base of the tree to the point where it broke as the adjacent side.

We can use the trigonometric function tangent to find the height at which the tree broke. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

Let's denote the height at which the tree broke as x. The tangent of the angle of 30 degrees is equal to the opposite side (x) divided by the adjacent side (24 - x). We can set up the following equation:

tan(30) = x / (24 - x)

To solve this equation, we can multiply both sides by (24 - x) and then solve for x.

Calculation

Let's calculate the value of x using the equation we derived:

tan(30) = x / (24 - x)

Taking the tangent of 30 degrees:

1/√3 = x / (24 - x)

Cross-multiplying:

x = (24 - x) / √3

Multiplying both sides by √3:

√3 * x = 24 - x

Adding x to both sides:

√3 * x + x = 24

Combining like terms:

(√3 + 1) * x = 24

Dividing both sides by (√3 + 1):

x = 24 / (√3 + 1)

Calculating the value of x:

x ≈ 24 / (1.732 + 1) ≈ 24 / 2.732 ≈ 8.79 meters

Answer

The tree broke at a height of approximately 8.79 meters.

Conclusion

In this problem, we used trigonometry to find the height at which a tree broke after being blown over by the wind. By setting up an equation using the tangent function, we were able to calculate the height at which the tree broke. The tree broke at a height of approximately 8.79 meters.