Question

Дана прямоугольная трапеция MNKL основания которой равны 5 и 8 см. Чему равна наибольшая сторона если один из углов равен 60 градусов?

Answer 1

Ответ:

Надеюсь, тебе будет понятен мой почерк)))

Объяснение:

Answer 2

Problem Analysis

We are given a rectangular trapezoid MNKL, with the lengths of its bases equal to 5 cm and 8 cm. One of the angles is 60 degrees. We need to find the length of the longest side.

Solution

To find the length of the longest side, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In our case, we can consider the trapezoid as a right triangle by drawing a perpendicular from one of the vertices to the base. Let's call the perpendicular line segment AD, where D is the point of intersection with the base KL. We can see that triangle ABD is a right triangle.

Now, we can use the Pythagorean theorem to find the length of AD. Let's denote the length of AD as x. According to the Pythagorean theorem, we have:

AB^2 = AD^2 + BD^2

Since one of the angles in the trapezoid is 60 degrees, we can use trigonometry to find the length of BD. In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In triangle ABD, we can use the sine of 60 degrees to find BD:

sin(60) = BD / AB

Since AB is the difference between the lengths of the bases, we have:

**BD = AB