Question

Поиск результатов по фразе "найдите диаметр окружности описанной около прямоугольника если его меньшая сторона равна 36 см а угол между диагоналями равен 60 градусов

Answer 1

Мне тоже вообще никто не помогает

Answer 2

Calculating the Diameter of the Circle Circumscribed around a Rectangle

To find the diameter of the circle circumscribed around a rectangle, we can use the formula:

Diameter = √(a^2 + b^2)

Where: - a and b are the sides of the rectangle - In this case, the smaller side of the rectangle is given as 36 cm

Given that the angle between the diagonals is 60 degrees, we can use the properties of a rectangle to find the length of the other side.

Calculating the Length of the Other Side of the Rectangle

The length of the other side of the rectangle can be calculated using the formula:

Other side = a * tan(θ)

Where: - a is the smaller side of the rectangle (36 cm) - θ is the angle between the diagonals (60 degrees)

Using these values, we can calculate the length of the other side of the rectangle.

Calculation

Using the given values: - Smaller side of the rectangle (a) = 36 cm - Angle between the diagonals (θ) = 60 degrees

We can calculate the length of the other side of the rectangle using the formula:

Other side = 36 * tan(60)

Result

Calculating the length of the other side: - Other side ≈ 36 * tan(60) ≈ 36 * √3 ≈ 36√3 cm

Calculating the Diameter of the Circle

Now that we have the lengths of both sides of the rectangle, we can calculate the diameter of the circle using the formula:

Diameter = √(a^2 + b^2)

Substituting the values: - Diameter = √(36^2 + (36√3)^2) - Diameter = √(1296 + 1296*3) - Diameter = √(1296 + 3888) - Diameter = √5184 - Diameter = 72 cm

So, the diameter of the circle circumscribed around the rectangle is 72 cm.