Question

Сторона трикутника дорівнює 35 см а дві інші утворюють кут 60° і відносяться як 8:3 яка довжина радіуса кола описана навколо даного трикутника

Answer 1

Объяснение:

відповідь та пояснення на фото.

Answer 2

Triangle Side Length and Angle

The given triangle has one side measuring 35 cm, and the other two sides form a 60° angle and are in a ratio of 8:3. We need to find the length of the radius of the circle circumscribed around this triangle.

Finding the Length of the Other Two Sides

To find the lengths of the other two sides, we can use the fact that they are in a ratio of 8:3. Let's assume the lengths of the other two sides are 8x and 3x, where x is a constant.

According to the given information, we have the equation: 8x + 3x + 35 = perimeter of the triangle

Since the perimeter of a triangle is the sum of its three sides, we can write: 8x + 3x + 35 = 2(8x + 3x)

Simplifying the equation, we get: 11x + 35 = 22x + 6x 11x + 35 = 28x

Solving for x, we find: 17x = 35 x = 35/17

Therefore, the lengths of the other two sides are approximately: 8x ≈ 8 * (35/17) cm 3x ≈ 3 * (35/17) cm

Finding the Radius of the Circumscribed Circle

To find the radius of the circle circumscribed around the triangle, we can use the formula:

Radius = (side1 * side2 * side3) / (4 * area)

The area of a triangle can be calculated using Heron's formula:

Area = sqrt(s * (s - side1) * (s - side2) * (s - side3))

where s is the semi-perimeter of the triangle, given by:

s = (side1 + side2 + side3) / 2

Substituting the values we have:

side1 = 35 cm side2 = 8x ≈ 8 * (35/17) cm side3 = 3x ≈ 3 * (35/17) cm

Calculating the semi-perimeter: s = (35 + 8 * (35/17) + 3 * (35/17)) / 2

Calculating the area: Area = sqrt(s * (s - 35) * (s - 8 * (35/17)) * (s - 3 * (35/17)))

Finally, substituting the values into the radius formula: Radius = (35 * 8 * (35/17) * 3 * (35/17)) / (4 * Area)

Please note that the above calculations are based on the given information and formulas for finding the radius of a circumscribed circle.