Question

В равнобедренной трапеции тупой угол равен 120 боковая сторона 12,меньшее осование равно высоте.Найти среднюю линию трапеции

Answer 1

Используй формулу средней линии трапеции.

Answer 2

Given Information:

We are given the following information about a trapezoid: - The trapezoid is isosceles. - The obtuse angle in the trapezoid is 120 degrees. - One of the lateral sides of the trapezoid measures 12 units. - The smaller base of the trapezoid is equal to its height.

Finding the Midline of the Trapezoid:

To find the midline of the trapezoid, we need to determine the length of the longer base. Since the trapezoid is isosceles, the longer base will be equal to the sum of the lengths of the two lateral sides.

Let's denote the length of the longer base as B and the length of the shorter base as b.

Since the trapezoid is isosceles, the opposite angles at the bases are congruent. Therefore, the acute angles at the bases are each equal to (180 - 120) / 2 = 30 degrees.

Using trigonometry, we can find the length of the longer base B by considering the right triangle formed by the height, the shorter base, and half of the longer base.

In this right triangle, the angle opposite the height is 30 degrees, and the side opposite this angle is b/2. The side adjacent to this angle is the height, which is equal to b.

Using the trigonometric function tangent, we can write the following equation:

tan(30) = (b/2) / b

Simplifying the equation, we get:

1/√3 = 1/2

From this equation, we can determine that b = 2/√3.

Since the smaller base is equal to the height, we have:

b = h

Now, we can find the length of the longer base B:

B = 2 * (b/2) + 12

Substituting the value of b:

B = 2 * (2/√3) + 12

Simplifying the equation, we get:

B = (4/√3) + 12

Therefore, the length of the longer base B is (4/√3) + 12.

Finally, to find the midline of the trapezoid, we take the average of the lengths of the two bases:

Midline = (B + b) / 2

Substituting the values of B and b:

Midline = ((4/√3) + 12 + 2/√3) / 2

Simplifying the equation, we get:

Midline = (16/√3 + 2/√3) / 2

Combining the terms with the same denominator, we have:

Midline = 18/√3 / 2

Simplifying further, we get:

Midline = 9/√3

Therefore, the midline of the trapezoid is 9/√3 units.

Answer:

The midline of the trapezoid is 9/√3 units.