Question

Дерево высотой 5,4 м стоит на расстоянии 14 шагов от дома, на котором установлен прожектор. Тень от дерева равна трём шагам. Какова высота дома в метрах?помогите, буду очень благодарен

Answer 1

Решается пропорцией.$\frac{5,4}{3}=\frac{x}{14+3}; x=30,6$

Answer 2

Calculating the Height of the House

To calculate the height of the house in meters, we can use the information provided about the tree, its shadow, and the distance between the tree and the house.

Given: - Height of the tree: 5.4 m - Distance between the tree and the house: 14 steps - Length of the tree's shadow: 3 steps

To find the height of the house, we can set up a proportion using similar triangles. The height of the tree and the length of its shadow form one triangle, while the height of the house and the length of its shadow form another triangle. Since the triangles are similar, we can set up the following proportion:

Height of the tree / Length of the tree's shadow = Height of the house / Length of the house's shadow

Plugging in the given values, we get:

5.4 m / 3 steps = Height of the house / Length of the house's shadow

To find the height of the house, we need to determine the length of the house's shadow. Since the tree is 14 steps away from the house and its shadow is 3 steps long, we can calculate the length of the house's shadow by subtracting the length of the tree's shadow from the distance between the tree and the house:

Length of the house's shadow = Distance between the tree and the house - Length of the tree's shadow = 14 steps - 3 steps = 11 steps

Now we can substitute the values into the proportion:

5.4 m / 3 steps = Height of the house / 11 steps

To solve for the height of the house, we can cross-multiply and divide:

Height of the house = (5.4 m / 3 steps) * 11 steps

Calculating this expression, we find that the height of the house is approximately 19.8 meters.

Please note that the above calculation assumes that the lengths of the tree's shadow and the house's shadow are proportional to their respective heights. It also assumes that the steps mentioned in the question are of equal length.