Question

В параллелограмме ABCD косинус B равен минус корень из 11 деленное на 6 высота опущенная на сторону AD D равно 5 Найдите CD

Answer 1

Решение в скане.............

Answer 2

Finding CD in a Parallelogram

To find the length of CD in parallelogram ABCD, we need to use the given information about the cosine of angle B and the height dropped onto side AD.

Let's break down the problem step by step:

1. Given information: - Cosine of angle B: cos(B) = -√11/6. - Height dropped onto side AD: h = 5.

2. Understanding the problem: - We have a parallelogram ABCD, where AB is parallel to CD and AD is parallel to BC. - We are given the cosine of angle B and the height dropped onto side AD. - We need to find the length of CD.

3. Solution: - In a parallelogram, the opposite sides are equal in length. Therefore, AB = CD. - We can use the cosine rule to find the length of AB (or CD) using the given information. - The cosine rule states that for a triangle with sides a, b, and c, and angle A opposite side a, the following equation holds: a^2 = b^2 + c^2 - 2bc * cos(A). - In our case, we can consider triangle ABD, where AB = c, AD = b, and angle B = A. - Using the cosine rule, we can write the equation as: AB^2 = AD^2 + BD^2 - 2 * AD * BD * cos(B). - Since AB = CD, we can rewrite the equation as: CD^2 = AD^2 + BD^2 - 2 * AD * BD * cos(B). - We are given AD = 5 and cos(B) = -√11/6. - We need to find BD to calculate CD.

4. Finding BD: - To find BD, we can use the Pythagorean theorem in triangle ABD. - The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. - In our case, triangle ABD is a right-angled triangle with AB as the hypotenuse, AD as one side, and BD as the other side. - Using the Pythagorean theorem, we can write the equation as: AB^2 = AD^2 + BD^2. - Since AB = CD and AD = 5, we can rewrite the equation as: CD^2 = 5^2 + BD^2. - Solving for BD, we get: BD^2 = CD^2 - 25.

5. Substituting values and solving for CD: - We know that cos(B) = -√11/6 and BD^2 = CD^2 - 25. - Substituting these values into the equation CD^2 = AD^2 + BD^2 - 2 * AD * BD * cos(B), we get: CD^2 = 5^2 + (CD^2 - 25) - 2 * 5 * BD * (-√11/6). - Simplifying the equation, we get: CD^2 = 25 + CD^2 - 25 + 5 * BD * √11/3. - Cancelling out the CD^2 terms, we get: 0 = 5 * BD * √11/3. - Dividing both sides by 5 * √11/3, we get: BD = 0. - Since BD = 0, we can conclude that CD = AB = 0.

Therefore, the length of CD in parallelogram ABCD is 0.

Please let me know if you need any further clarification or assistance!