Question

Человек ростом 1,5 м стоит на расстоянии 12 м от столба, на вершине которого висит фонарь. Найдите высоту столба, если длина отбрасываемой этим человеком тени равна 3 м

Answer 1

треугольник - человек, его тень, и малая гепотенуза - подобен труегольнику - столб, его тень, большая гипотенуза. следовательно  1.5/ 12 = х/ 3, где х - высота столба. получили 24

Answer 2

Problem Analysis

We are given that a person with a height of 1.5 meters is standing 12 meters away from a pole. The person's shadow is 3 meters long. We need to find the height of the pole.

Solution

Let's assume the height of the pole is h meters.

From the given information, we can form a right triangle with the person, the pole, and the shadow. The person's height is one side of the triangle, the shadow is the base, and the distance between the person and the pole is the hypotenuse.

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

h / 1.5 = (h + 3) / 12

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

Calculation

Cross-multiplying the equation, we get:

12h = 1.5(h + 3)

Expanding the equation:

12h = 1.5h + 4.5

Subtracting 1.5h from both sides:

10.5h = 4.5

Dividing both sides by 10.5:

h = 4.5 / 10.5

Evaluating the expression:

h ≈ 0.4286

Answer

The height of the pole is approximately 0.4286 meters.

Verification

To verify the answer, we can substitute the calculated value of h back into the original equation and check if it holds true.

0.4286 / 1.5 = (0.4286 + 3) / 12

Simplifying the equation:

0.2857 ≈ 3.4286 / 12

0.2857 ≈ 0.2857

The equation holds true, confirming that the calculated height of the pole is correct.