Question

ABCD-Параллелограмм его стороны равны 6 и 8 см.Остры угол 60 градусов.Найти высоты проведенные из 1 вершины смежным сторонам

Answer 1

АВСD - паралелограмм. АВ=6см, AD=8см.  Угол А=60. ВН и ВЕ - высоты, проведенные к сторонам АD и СD.  Площадь паралелограмма найдем по формуле:

S=AB*AD*sin60=6*8*√3/2=24√3см^2

А еще площадь паралелограмма - это произведение его стороны на высоту, проведенную к этой стороне. Отсюда найдем его высоты:

ВН=24√3/8=3√3см

ВЕ=24√3/6=4√3см

Answer 2

Given Information

We are given that ABCD is a parallelogram with sides measuring 6 cm and 8 cm. We are also told that one of the acute angles in the parallelogram measures 60 degrees. We need to find the heights drawn from one vertex to the adjacent sides.

Solution

To find the heights drawn from one vertex to the adjacent sides, we can use the formula for the area of a parallelogram. The area of a parallelogram is given by the formula:

Area = base * height

In this case, the base of the parallelogram is the side adjacent to the height we want to find, and the height is the distance from the vertex to the opposite side.

Let's label the vertices of the parallelogram as follows: A - the vertex from which the heights are drawn B - the adjacent vertex C - the opposite vertex to A D - the opposite vertex to B

We are given that AB = 6 cm and BC = 8 cm. We need to find the heights drawn from vertex A to sides BC and AD.

To find the height drawn from vertex A to side BC, we can use the formula for the area of a parallelogram:

Area = base * height

The base is BC, which is 8 cm. We can rearrange the formula to solve for the height:

Height = Area / Base

The area of the parallelogram can be calculated using the formula:

Area = AB * height

Substituting the values we know:

Area = 6 cm * height

Now we can substitute this expression for the area into the formula for the height:

Height = (6 cm * height) / 8 cm

Simplifying the expression:

Height = 3/4 * height

To find the height drawn from vertex A to side AD, we can use the same formula:

Area = base * height

The base is AD, which is also 6 cm. We can rearrange the formula to solve for the height:

Height = Area / Base

The area of the parallelogram can be calculated using the formula:

Area = AB * height

Substituting the values we know:

Area = 6 cm * height

Now we can substitute this expression for the area into the formula for the height:

Height = (6 cm * height) / 6 cm

Simplifying the expression:

Height = height

Therefore, the height drawn from vertex A to side AD is equal to the height itself.

To summarize: - The height drawn from vertex A to side BC is 3/4 * height. - The height drawn from vertex A to side AD is height.

Please note that we do not have the exact value for the height since we do not know the exact dimensions of the parallelogram. However, we can express the heights in terms of the height itself.

Let me know if you need any further assistance!