Question

В ТРЕУГОЛЬНИКЕ АВС УГОЛ DEB =60 ГРАДУСОВ,ВЕ=3 и средняя линия DE=2. Найти сторону АВ.

Answer 1

DE сред. линия ⇒ BC=2*BE=2*3=6см и AC=2*DE=2*2=4 см и угол С=углу E=60

по т. косинусов:

AB²=BC²+AC²-2*AC*BC*Cosγ

AB²=6²+4²-2*6*4*Cos60

AB²=36+16-48*(1/2)

AB²=52-24

AB²=28

AB=√28=2√7 см

 

сторона AB равна 2√7 см

 

Answer 2

Finding the length of side AB in triangle ABC

To find the length of side AB in triangle ABC, we can use the given information about the triangle. Let's break down the information provided:

- Angle DEB = 60 degrees - Side VE = 3 - The length of the median DE = 2

To solve for the length of side AB, we need to use the properties of triangles and apply the appropriate formulas.

Using the properties of triangles to find side AB

In triangle ABC, we can use the fact that the median of a triangle divides the opposite side into two equal segments. This means that DE is divided into two equal segments, each measuring 1.

Let's denote the point where the median DE intersects side AB as point M. Since DE is divided into two equal segments, we can say that AM = MB = 1.

Now, let's consider triangle AEM. We know that angle DEB = 60 degrees, and since DE is a median, angle DEM is a right angle. Therefore, angle DEM = 90 degrees.

Using the given information, we can apply trigonometric ratios to find the length of side AB.

Applying trigonometric ratios to find side AB

In triangle AEM, we have the following information:

- Angle DEM = 90 degrees - Angle DEA = 60 degrees - Side VE = 3 - Side AM = 1

We can use the trigonometric ratio for the sine of an angle to find the length of side AE:

sin(DEA) = AE / VE

Rearranging the equation, we get:

AE = VE * sin(DEA)

Substituting the given values, we have:

AE = 3 * sin(60)

Using the trigonometric values for a 60-degree angle, we find that sin(60) = √3 / 2. Substituting this value, we get:

AE = 3 * (√3 / 2) = (3√3) / 2

Since AM = 1, we can find the length of side AB by adding AE and AM:

AB = AE + AM = (3√3) / 2 + 1

Therefore, the length of side AB in triangle ABC is (3√3) / 2 + 1.

Please note that the exact numerical value of side AB cannot be determined without knowing the specific values of VE and DE. However, the expression (3√3) / 2 + 1 represents the length of side AB in terms of the given variables.

I hope this helps! Let me know if you have any further questions.