Question

Тень от вертикально установленного шеста высотой 90 см отбрасывает освещённую уличным фонарём тень длиной 120 см, если установить шест на 1 м дальше от фонаря,то длина тени составит 150 см. На какой высоте весит фонарь?

Answer 1

Задача сугубо геометрического свойства
Высота фонаря h
исходное расстояние от фонаря до шеста z
Всё в метрах.
Слева - картинка до, справа - после
из подобия треугольников
h/(z+1.2) = 0.9/1.2
h/(z+1+1.5) = 0.9/1.5
---
h = 3/4*(z+1.2)
h = 3/5*(z+2.5)
---
3/4*(z+1.2) = 3/5*(z+2.5)
5(z+1.2) = 4(z+2.5)
5z + 6 = 4z +10
z = 4 метров
h = 3/4*(z+1.2) = 3/4*5.2 = 3.9 метров

Answer 2

Calculation of the Height of the Lamp Post

To determine the height of the lamp post, we can use the concept of similar triangles. Let's denote the height of the lamp post as h.

According to the given information, when the lamp post is vertically installed at a height of 90 cm, it casts a shadow that is 120 cm long. When the lamp post is moved 1 meter further away from the lamp, the length of the shadow increases to 150 cm.

We can set up the following proportion to find the height of the lamp post:

90 cm / 120 cm = (90 cm + h) / 150 cm

To solve this proportion, we can cross-multiply and then solve for h:

90 cm * 150 cm = 120 cm * (90 cm + h)

Simplifying the equation:

13500 cm^2 = 10800 cm^2 + 120 cm * h

2700 cm^2 = 120 cm * h

Dividing both sides of the equation by 120 cm:

2700 cm^2 / 120 cm = h

22.5 cm = h

Therefore, the height of the lamp post is 22.5 cm.

Please note that the search results provided by You.com did not contain relevant information for this specific calculation. The calculation was performed using mathematical principles.