Question

В прямоугольной трапеции острый угол равен 60°. Большая боковая сторона и большее основание равны по 12 см. Найдите среднюю линию трапеции. С ПОДРОБНЫМ ОБЪЯСНЕНИЕМ ПОЖАЛУЙСТА!

Answer 1

вот и ответ. . . . . . . . . . . . . . . . . . . . .

Answer 2

Problem Analysis

We are given a trapezoid with an acute angle of 60°. The larger side and the larger base of the trapezoid are both 12 cm. We need to find the length of the median of the trapezoid.

Solution

To find the length of the median of a trapezoid, we can use the formula:

Median = (Sum of the lengths of the bases) / 2

In this case, the sum of the lengths of the bases is equal to the sum of the larger base and the smaller base. Since the problem statement only provides the length of the larger base, we need to find the length of the smaller base.

To find the length of the smaller base, we can use the fact that the acute angle of the trapezoid is 60°. In a trapezoid, the angles at the bases are supplementary. Therefore, the angle at the smaller base is 180° - 60° = 120°.

Now, we can use trigonometry to find the length of the smaller base. Let's consider the right triangle formed by the smaller base, the height of the trapezoid, and the line segment connecting the midpoint of the smaller base to the midpoint of the larger base.

Let's denote the length of the smaller base as b, the length of the larger base as B, and the height of the trapezoid as h.

In the right triangle, the side opposite the angle of 60° is the height of the trapezoid, and the side adjacent to the angle of 60° is half the difference between the lengths of the bases.

Using the trigonometric ratio for the tangent of an angle, we have:

tan(60°) = h / ((B - b) / 2)

Simplifying the equation, we get:

h = ((B - b) / 2) * tan(60°)

Now, we can substitute the given values into the equation to find the height of the trapezoid.

Finally, we can substitute the values of the lengths of the bases and the height into the formula for the median to find the length of the median.

Let's calculate the length of the median step by step.

Calculation

Given: - Larger base (B) = 12 cm - Acute angle = 60°

Step 1: Finding the length of the smaller base (b) - The angle at the smaller base is 180° - 60° = 120°. - We can use trigonometry to find the length of the smaller base. - Let's assume the height of the trapezoid is h. - Using the tangent function, we have: tan(60°) = h / ((B - b) / 2) - Rearranging the equation, we get: h = ((B - b) / 2) * tan(60°) - Substituting the values, we have: h = ((12 - b) / 2) * tan(60°)

Step 2: Finding the length of the median - The median is the average of the lengths of the bases. - The sum of the lengths of the bases is B + b. - Therefore, the length of the median is (B + b) / 2. - Substituting the values, we have: Median = (12 + b) / 2

Now, let's calculate the length of the median using the given information.

Calculation

Step 1: Finding the length of the smaller base (b) - Using the equation h = ((12 - b) / 2) * tan(60°), we need to find the value of h. - However, we don't have the value of h or b, so we cannot calculate the length of the median.

Unfortunately, without the value of the height or the length of the smaller base, we cannot determine the length of the median of the trapezoid.