Question

Помогите, пожалуйста.....Человек стоит на расстоянии 5,6 м от столба, на котором висит фонарь, расположенный на высоте 4,5 м. Тень человека равна 3,4 м. Какого роста человек( в метрах)?

Answer 1

x:3,4=4,5:(3,4+5,6)
x:3,4=4,5:9
x:3,4=0,5
x=1,7 метра - рост человека

Answer 2

Calculation of the person's height

To calculate the height of the person, we can use similar triangles. The person, the shadow, and the height of the lamppost form a right triangle. The height of the person can be determined by finding the ratio of the lengths of the corresponding sides of the two triangles.

Let's denote the height of the person as x meters.

The given information is as follows: - The person is standing at a distance of 5.6 meters from the lamppost. - The lamppost is 4.5 meters tall. - The length of the shadow cast by the person is 3.4 meters.

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

x / 3.4 = (x + 4.5) / 5.6

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

5.6x = 3.4(x + 4.5)

Simplifying the equation:

5.6x = 3.4x + 15.3

5.6x - 3.4x = 15.3

2.2x = 15.3

x = 15.3 / 2.2

x ≈ 6.9545

Therefore, the height of the person is approximately 6.9545 meters.