Question

В трапеции АВСД угол А равен 90°, угол С равен 150°, ВС равен 2 см, диагональ АС перпендкулярна боковой стороне СД. Найдите среднюю линию трапеции.

Answer 1

5. Сначало находим диагонал. Потом нижнее основание и их полусумма равна ср линии

Answer 2

Finding the Length of the Median of a Trapezoid

In order to find the length of the median of a trapezoid, we can use the formula:

Median = 1/2 * (Sum of the lengths of the bases)

Given the trapezoid ABCD, where angle A = 90°, angle C = 150°, BC = 2 cm, and diagonal AC is perpendicular to the side CD, we can find the length of the median using the formula mentioned above.

First, we need to find the lengths of the bases of the trapezoid.

Finding the Lengths of the Bases

To find the lengths of the bases, we can use the information provided in the question and apply trigonometric concepts.

We know that the diagonal AC is perpendicular to the side CD, and angle A = 90°. This means that triangle ACD is a right-angled triangle.

Using trigonometric ratios, we can find the lengths of the sides AC and AD.

Using Trigonometric Ratios to Find the Lengths of the Sides

We can use the given information to find the lengths of the sides AC and AD. Once we have the lengths of the bases, we can calculate the median of the trapezoid using the formula mentioned earlier.

Let's proceed with finding the lengths of the bases and then calculating the median of the trapezoid.