Question

B параллелограмме MFKS MF относится к Мк как 1:2 и 25км равен 38°. Найдите наименьший из углов, образованных диагоналями параллелограмма. Ответ дайте в градусах.​

Answer 1

Ответ:

71

Объяснение:

_--__-__-_-_

Answer 2

Parallelogram and Diagonals

A parallelogram is a quadrilateral with opposite sides that are parallel. In the given problem, we have a parallelogram MFKS, where MF is related to MK as 1:2 and the length of MF is 25 km. We are asked to find the smallest angle formed by the diagonals of the parallelogram.

Solution

To find the smallest angle formed by the diagonals of the parallelogram, we can use the properties of parallelograms and trigonometry.

Let's denote the intersection point of the diagonals as O. Since the diagonals of a parallelogram bisect each other, we can say that MO = OK.

Now, let's consider triangle MFO. We know that MF = 25 km and MK = 2 * MF = 2 * 25 km = 50 km. We are also given that the angle MFK is 38°.

Using the Law of Cosines, we can find the length of FO: ``` FO^2 = MF^2 + MO^2 - 2 * MF * MO * cos(MFK) FO^2 = 25^2 + MO^2 - 2 * 25 * MO * cos(38°) ```

Similarly, using the Law of Cosines in triangle MKO, we can find the length of KO: ``` KO^2 = MK^2 + MO^2 - 2 * MK * MO * cos(MFK) KO^2 = 50^2 + MO^2 - 2 * 50 * MO * cos(38°) ```

Since MO = OK, we can equate the two expressions for FO^2 and KO^2: ``` 25^2 + MO^2 - 2 * 25 * MO * cos(38°) = 50^2 + MO^2 - 2 * 50 * MO * cos(38°) ```

Simplifying the equation, we get: ``` 625 - 50 * MO * cos(38°) = 2500 - 100 * MO * cos(38°) 50 * MO * cos(38°) = 2500 - 625 50 * MO * cos(38°) = 1875 MO * cos(38°) = 1875 / 50 MO * cos(38°) = 37.5 ```

Now, we can find the value of MO: ``` MO = 37.5 / cos(38°) MO ≈ 47.71 km ```

Since MO = OK, we can conclude that the diagonals of the parallelogram are congruent.

Finally, let's find the smallest angle formed by the diagonals. We can use the Law of Cosines in triangle MFO: ``` cos(MOF) = (MF^2 + FO^2 - MO^2) / (2 * MF * FO) cos(MOF) = (25^2 + FO^2 - 47.71^2) / (2 * 25 * FO) ```

Simplifying the equation, we get: ``` cos(MOF) = (625 + FO^2 - 2276.64) / (50 * FO) cos(MOF) = (FO^2 - 1651.64) / (50 * FO) ```

Since MO = OK, we can substitute FO with MO in the equation: ``` cos(MOF) = (MO^2 - 1651.64) / (50 * MO) cos(MOF) = (47.71^2 - 1651.64) / (50 * 47.71) ```

Calculating the value of cos(MOF), we get: ``` cos(MOF) ≈ 0.9999 ```

To find the smallest angle MOF, we can take the inverse cosine (arccos) of cos(MOF): ``` MOF ≈ arccos(0.9999) MOF ≈ 0.014° ```

Therefore, the smallest angle formed by the diagonals of the parallelogram MFKS is approximately 0.014°.

Note: The calculations provided are based on the given information and assumptions made about the properties of the parallelogram.