Question

Сторона треугольника равна 26 см а две другие образуют угол 60 градусов и относятся как 8:3. Найти наименьшую высоту и радиусы вписаной и описаной окружности для этого треугольника Помогите пожалуйста!!

Answer 1

Длина одной стороны у нас равна 26 см
обозначим вторую и третью как 8х см и 3х см (это исходя из их отношения)
по т. косинусов имеем: 
26² = (8х)² +(3х)² - 2* 8х *3х *cos60° 
676 = 64x² + 9x² -48x² *1/2 
676 = 25х²
х² = 676/25
х = √(676/25) = 26/5

значит вторая сторона треуголлника = 8х = 8 *26/5 = 208/5 см
третья сторона = 3х = 3*26/5 = 78/5 см
периметр = 26 + 208/7 + 78/7 = 26+57,2 = 83,2 см

Answer 2

Given Information

We are given that one side of a triangle is 26 cm, and the other two sides form a 60-degree angle and are in a ratio of 8:3. We need to find the minimum height and the radii of the inscribed and circumscribed circles for this triangle.

Finding the Lengths of the Other Two Sides

Let's assume the lengths of the other two sides are 8x and 3x, where x is a constant. Since the sides are in a ratio of 8:3, we can write the following equation:

8x + 3x + 26 = perimeter of the triangle

To find the perimeter, we need to know the lengths of all three sides. Since we only know one side (26 cm), we cannot determine the exact perimeter or the lengths of the other two sides. Therefore, we cannot proceed with finding the minimum height or the radii of the inscribed and circumscribed circles for this triangle.

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