Question

Человек ростом 1,5м стоит на расстоянии 6 м от столба,на котором висит фонарь на высоте 4,5 м. Найдите длину тени человека, в метрах.

Answer 1

х - длина тени. составляем пропорцию

4,5/1.5=(6+х)/х

3х=6+х    х=3

Answer 2

Calculation of Shadow Length

To find the length of the shadow cast by a person standing at a distance from a pole with a hanging lantern, we can use similar triangles. Let's break down the given information:

- Height of the person: 1.5 meters - Distance of the person from the pole: 6 meters - Height of the pole with the lantern: 4.5 meters

We can create two similar triangles: one formed by the person, their shadow, and the distance from the pole, and another formed by the pole, the lantern, and the length of the shadow.

Let's denote the length of the shadow as x.

Using the concept of similar triangles, we can set up the following proportion:

1.5 / x = 6 / (x + 4.5)

To solve for x, we can cross-multiply and solve the resulting equation.

1.5 * (x + 4.5) = 6 * x

1.5x + 6.75 = 6x

6.75 = 6x - 1.5x

6.75 = 4.5x

x = 6.75 / 4.5

x = 1.5

Therefore, the length of the shadow cast by the person is 1.5 meters.