Question

Стороны параллелограмма 4см и 5 см Острый угол 60°. Найти его диагонали.

Answer 1

Решение смотри во вложении

Answer 2

Given Information:

We are given that the sides of the parallelogram are 4 cm and 5 cm, and one of the acute angles is 60°. We need to find the diagonals of the parallelogram.

Solution:

To find the diagonals of the parallelogram, we can use the properties of a parallelogram. In a parallelogram, opposite sides are equal in length, and opposite angles are equal in measure.

Since we know the sides of the parallelogram are 4 cm and 5 cm, we can conclude that the opposite sides are also 4 cm and 5 cm.

Let's label the sides of the parallelogram as follows: - Side AB = 4 cm - Side BC = 5 cm

Since opposite sides of a parallelogram are equal, we can conclude that side CD is also 4 cm and side AD is also 5 cm.

Now, let's find the diagonals of the parallelogram.

Diagonal AC:

To find diagonal AC, we can use the cosine rule. The cosine rule states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we have a triangle with sides AC, AB, and BC, and angle ABC opposite side BC.

Using the cosine rule, we can find the length of diagonal AC:

AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(ABC)

Substituting the known values:

AC^2 = 4^2 + 5^2 - 2 * 4 * 5 * cos(60°)

Simplifying the equation:

AC^2 = 16 + 25 - 40 * cos(60°)

AC^2 = 41 - 40 * 0.5

AC^2 = 41 - 20

AC^2 = 21

Taking the square root of both sides:

AC = √21

So, the length of diagonal AC is approximately 4.58 cm.

Diagonal BD:

To find diagonal BD, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In our case, we have a right triangle with sides BD, AB, and AD.

Using the Pythagorean theorem, we can find the length of diagonal BD:

BD^2 = AB^2 + AD^2

Substituting the known values:

BD^2 = 4^2 + 5^2

BD^2 = 16 + 25

BD^2 = 41

Taking the square root of both sides:

BD = √41

So, the length of diagonal BD is approximately 6.40 cm.

Summary:

The diagonals of the parallelogram are approximately: - Diagonal AC: 4.58 cm - Diagonal BD: 6.40 cm

Please note that the values are approximate due to rounding.

Let me know if there's anything else I can help you with!