Question

У прямокутній системі координат на площині задано паралелограм АВСD, cos A = 0,44. Визначте довжину Діагоналі в паралелограма, якщо скалярний добуток векторів → АВ(6; -8) і AD дорівнює 88​

Answer 1

Ответ:

Пошаговое объясненитвоашашашкшшклкллклклкщад

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Answer 2

Given that in a rectangular coordinate system on the plane, a parallelogram ABCD is defined and cos a = 0.44. We need to determine the length of the diagonal in the parallelogram if the dot product of the vectors → AB(6, -8) and → ad is equal to 88.

First, let's find the length of vector → AB. We can use the Pythagorean theorem: |→ AB| = √((6^2) + (-8^2)) = √(36 + 64) = √100 = 10

Next, let's find the angle between vectors → AB and → ad. We know that the dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them. So we can write: → AB · → ad = |→ AB| * |→ ad| * cos a

Substituting the given values, we have: 88 = 10 * |→ ad| * 0.44 |→ ad| = 88 / (10 * 0.44) ≈ 20

Now, let's find the length of vector → ad. We know that the length of vector → ad is equal to the length of vector → AB multiplied by the sine of the angle between them. Since they are vectors in a parallelogram, the angle between → AB and → ad is the complement of angle a. Therefore, we have: |→ ad| = |→ AB| * sin(90° - a)

Using the given value of cos a, we can calculate sin a: sin a = √(1 - cos^2 a) = √(1 - 0.44^2) ≈ 0.89

Now we can calculate |→ ad|: |→ ad| = 10 * sin(90° - a) = 10 * sin(90° - arccos(0.44)) ≈ 10 * sin(arcsin(0.89)) ≈ 10 * 0.89 ≈ 8.9

Therefore, the length of the diagonal in the parallelogram ABCD is approximately 8.9.