Question

(по теореме синусов)острый угол ромба =120 сторона = 7. найдите диагонали.​

Answer 1

Ответ:

Вложение

Объяснение:

Вложение

Answer 2

Theorem of Sines

The theorem of sines relates the lengths of the sides of a triangle to the sines of its angles. It states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Mathematically, the theorem of sines can be expressed as follows:

a/sin(A) = b/sin(B) = c/sin(C)

Where: - a, b, and c are the lengths of the sides of the triangle. - A, B, and C are the measures of the angles opposite to sides a, b, and c, respectively.

In this case, we have an acute-angled rhombus with an angle measure of 120 degrees and a side length of 7 units. We need to find the lengths of the diagonals.

Finding the Diagonals of the Rhombus

To find the lengths of the diagonals of the rhombus, we can use the theorem of sines. Since a rhombus has all sides equal in length, we can consider one side of the rhombus as the base of a triangle. Let's call this side 'a'.

In the given rhombus, the angle opposite to side 'a' is 120 degrees. Therefore, we can write the following equation using the theorem of sines:

a/sin(120) = d1/sin(A)

Where: - d1 is the length of one diagonal of the rhombus. - A is the measure of the angle between the diagonals.

Since the diagonals of a rhombus bisect each other at right angles, the measure of angle A is 90 degrees.

Now, let's substitute the values into the equation:

7/sin(120) = d1/sin(90)

Using the values of sin(120) and sin(90) from trigonometric tables, we can calculate the length of one diagonal, d1.

Calculation

Using the values of sin(120) and sin(90), we can calculate the length of one diagonal, d1.

sin(120) ≈ 0.866 sin(90) = 1

Substituting the values into the equation:

7/0.866 = d1/1

Simplifying the equation:

d1 ≈ 8.08

Therefore, the length of one diagonal of the rhombus is approximately 8.08 units.

To find the length of the other diagonal, we can use the fact that the diagonals of a rhombus are equal in length. Therefore, the length of the other diagonal is also approximately 8.08 units.

Answer

The lengths of the diagonals of the given rhombus are approximately 8.08 units each.

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