Question

Помогите пожалуйста. В ромбе сторона равна 10, одна из диагоналей — 10, а угол, лежащий напротив этой диагонали, равен 60°. Найдите площадь ромба, деленную на корень 3 . 15.02.2015

Answer 1

Problem Analysis

We are given the following information about a rhombus: - One side of the rhombus is 10 units long. - One of the diagonals is 10 units long. - The angle opposite to this diagonal is 60°.

We need to find the area of the rhombus divided by the square root of 3.

Solution

To find the area of the rhombus, we can use the formula: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.

Let's calculate the length of the other diagonal using the given information. Since one of the diagonals is 10 units long, we can use the properties of a rhombus to find the length of the other diagonal.

In a rhombus, the diagonals are perpendicular bisectors of each other. This means that they intersect at a right angle and divide each other into two equal parts.

Since one of the diagonals is 10 units long, the other diagonal will also be 10 units long.

Now, we can calculate the area of the rhombus using the formula mentioned earlier:

Area = (d1 * d2) / 2 = (10 * 10) / 2 = 100 / 2 = 50 square units

To find the area of the rhombus divided by the square root of 3, we divide the area by the square root of 3:

Area / √3 = 50 / √3

Let's calculate the approximate value of this expression.

Calculation

To calculate the approximate value of 50 / √3, we can use a calculator or perform the division manually.

Using a calculator, the approximate value of 50 / √3 is 28.8675 (rounded to four decimal places).

Therefore, the area of the rhombus divided by the square root of 3 is approximately 28.8675.

Please note that the date provided in your question, "15.02.2015," does not have any relevance to the solution of the problem.