Question

Точка крепления троса, удерживающего флагшток в вертикальном положении, находится на высоте 15 м от земли. Расстояние от основания флагштока до места крепления троса на земле равно 8 м. Найдите длину троса. Ответ дайте в метрах.

Answer 1

To find the length of the rope, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the rope acts as the hypotenuse, and the distance from the base of the flagpole to the point where the rope is attached on the ground forms one of the legs of the right triangle. The height of the attachment point of the rope from the ground forms the other leg of the right triangle.

Let's denote the length of the rope as x, the distance from the base of the flagpole to the point where the rope is attached on the ground as a, and the height of the attachment point of the rope from the ground as b.

According to the given information, a = 8 m and b = 15 m.

Using the Pythagorean theorem, we can write the equation:

x^2 = a^2 + b^2

Substituting the given values, we have:

x^2 = 8^2 + 15^2

Simplifying the equation:

x^2 = 64 + 225

x^2 = 289

Taking the square root of both sides:

x = √289

x = 17

Therefore, the length of the rope is 17 meters.

[[1]]