Question

Кути при вершині рівнобедреного трикутника =120° а його площа 20√3 м² Знайти сторони трикутника​

Answer 1

Ответ:

4корень5 м ; 4корень5 м ; 4корень15 м

Объяснение:

S=(b^2×sin<A) /2

2S=b^2×sin120

b=корень (2S/sin120)=

=корень ((2×20корень3) /(корень3 /2)) =

=корень (4×20)=корень 80=4корень5 м

<В=(180-<А):2=(180-120):2=30 градусов

cos<B=(a/2):b

a/2=b×cosB=b×cos30=

=4корень5×(корень3/2)=2корень15 м

а=2×2корень15=4корень15 м

Answer 2

I can understand and communicate fluently in Ukrainian. I will try to answer your question in detail.

The question is about finding the sides of an isosceles triangle with a vertex angle of 120° and an area of 20√3 m². To solve this problem, we can use the following steps:

1. Let the base of the triangle be c and the equal sides be a. Then the height of the triangle is h = a sin 60°, where 60° is half of the vertex angle. 2. The area of the triangle is given by S = (c h) / 2. Substituting the values of S and h, we get 20√3 = (c a sin 60°) / 2. 3. Simplifying the equation, we get c = (40√3) / (a sin 60°). We can use this expression to find c in terms of a. 4. To find a, we can use the Pythagorean theorem for the right triangle formed by the height and half of the base. We have a² = (c / 2)² + h², or a² = (c / 2)² + (a sin 60°)². 5. Substituting the expression for c, we get a² = ((40√3) / (2 a sin 60°))² + (a sin 60°)². Simplifying and rearranging, we get a⁴ - 80 a² + 1600 = 0. 6. This is a quadratic equation in a², which can be solved by factoring or using the quadratic formula. The positive root is a² = 40 + 20√3, which implies a = √(40 + 20√3). 7. Using the expression for c, we get c = (40√3) / (√(40 + 20√3) sin 60°). Simplifying, we get c = 2√(40 + 20√3).

Therefore, the sides of the triangle are a = √(40 + 20√3) m and c = 2√(40 + 20√3) m. You can check your answer by calculating the area of the triangle using these values and verifying that it is equal to 20√3 m².

You can also find similar problems and solutions on the web. I hope this helps you. Have a nice day!