Question

Диоганаль прямоугольника образует 65градусов с одной из её сторон . найдите острый угол между диагоналями этого прямоугольника

Answer 1

25 градусов, тк в прямоугольнике 4 угла по 90. Сл-но из одного угла вычитаем 65. получится 25

Answer 2

Finding the acute angle between the diagonals of a rectangle

To find the acute angle between the diagonals of a rectangle, we can use the relationship between the diagonals and the sides of the rectangle.

Given: - The diagonal of the rectangle forms a 65-degree angle with one of its sides.

Solution:

Let's denote the length of the diagonals as d1 and d2, and the length of the sides as a and b.

We know that the diagonals of a rectangle are of equal length, so d1 = d2.

The relationship between the diagonals and the sides of a rectangle can be expressed using the following trigonometric relationship:

d1^2 = a^2 + b^2

Given that the diagonal forms a 65-degree angle with one of its sides, we can use trigonometric functions to find the acute angle between the diagonals.

Using the cosine function: cos(65°) = a / d1

Solving for a: a = d1 * cos(65°)

Similarly, using the sine function: sin(65°) = b / d1

Solving for b: b = d1 * sin(65°)

Now, we can substitute the expressions for a and b into the relationship d1^2 = a^2 + b^2 to find the value of d1.

After finding the value of d1, we can use the relationship between the diagonals and the acute angle to find the acute angle between the diagonals.

Let's calculate the value of d1 and the acute angle between the diagonals.