Question

радіус кола описаного навколо рівнобедреного трикутника з кутом 120° дорівнює 8√3 знайдіть сторони трикутника.​

Answer 1

Відповідь:

Пояснення:

a =2*R*sin A =2*8*$\sqrt{3}$ *sin 120 = 24

b =2*R*sin B =2*8*$\sqrt{3}$ *sin 30 = 8$\sqrt{3}$

c =2*R*sin C =2*8*$\sqrt{3}$ *sin 30 = 8$\sqrt{3}$

Answer 2

Radius of the Circumscribed Circle

To find the sides of a triangle, we first need to determine the radius of the circumscribed circle. The radius of the circumscribed circle can be calculated using the formula:

R = a / (2 * sin(A))

Where: - R is the radius of the circumscribed circle - a is the length of any side of the triangle - A is the angle opposite to side a

In this case, we have a triangle with an angle of 120°. Let's assume that the length of each side of the triangle is a. Using the formula above, we can calculate the radius of the circumscribed circle:

R = a / (2 * sin(120°))

To simplify the calculation, we can use the fact that sin(120°) = sin(60°) = √3 / 2. Substituting this value into the formula, we get:

R = a / (2 * (√3 / 2)) = a / √3

Given that the radius of the circumscribed circle is 8√3, we can set up the following equation:

8√3 = a / √3

To solve for a, we can multiply both sides of the equation by √3:

8√3 * √3 = a

Simplifying the equation, we get:

24 = a

Therefore, the length of each side of the triangle is 24.

Conclusion

The sides of the equilateral triangle are all equal and have a length of 24 units.