Question

Вычисли сторону и площадь равностороннего треугольника, если радиус окружности, описанной около данного треугольника, равен 9 дм Чему равен АВ Чему равен S

Answer 1

ΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞ

Answer 2

Calculating the Side and Area of an Equilateral Triangle

To calculate the side and area of an equilateral triangle when the radius of the circumscribed circle is 9 dm, we can use the following steps:

1. Calculating the Side (AB): - The formula for the side of an equilateral triangle in terms of the radius of the circumscribed circle is given by: AB = 2 * R * sin(60°), where R is the radius of the circumscribed circle. - Substituting the given radius (R = 9 dm) into the formula: AB = 2 * 9 * sin(60°). - Calculating the value of AB using the given formula and trigonometric function: AB = 2 * 9 * 0.866. - Therefore, the side of the equilateral triangle (AB) is approximately 15.588 dm.

2. Calculating the Area (S): - The formula for the area of an equilateral triangle in terms of the side length is given by: S = (AB^2 * √3) / 4, where AB is the side length. - Substituting the calculated side length (AB ≈ 15.588 dm) into the formula: S = (15.588^2 * √3) / 4. - Calculating the value of S using the given formula: S ≈ (15.588^2 * 1.732) / 4. - Therefore, the area of the equilateral triangle (S) is approximately 94.991 dm^2.

So, the side length (AB) of the equilateral triangle is approximately 15.588 dm, and the area (S) is approximately 94.991 dm^2.