В треугольнике ABC AB=BC=AC=46 √ 3 найдите высоту CH

Для нахождения высоты треугольника CH можно воспользоваться формулой высоты в равностороннем треугольнике: h = (a√3)/2, где a - сторона треугольника. Подставляем значение стороны треугольника AB = BC = AC = 46√3 и получаем: h = (46√3 √3) / 2 = 46 3 / 2 = 69. Таким образом, высота треугольника CH равна 69.

В данном случае треугольник ABC является равносторонним, так как все его стороны равны: ( AB = BC = AC = 46\sqrt{3} ).

Для нахождения высоты CH в равностороннем треугольнике можно воспользоваться формулой для высоты, которая выражается через сторону треугольника:

[ h = \frac{\sqrt{3}}{2} \cdot a ]

где ( a ) — длина стороны треугольника. Подставим значение стороны:

[ h = \frac{\sqrt{3}}{2} \cdot 46\sqrt{3} ]

Упростим выражение:

1. Умножим числа под корнем: (\sqrt{3} \cdot \sqrt{3} = 3).
2. Теперь имеем: ( h = \frac{\sqrt{3}}{2} \cdot 46 \cdot \sqrt{3} = \frac{3}{2} \cdot 46 = \frac{138}{2} = 69 ).

Таким образом, высота CH в данном равностороннем треугольнике равна 69.

Для нахождения высоты треугольника CH можно воспользоваться формулой для высоты, которая связана с площадью треугольника. Площадь треугольника можно найти, используя формулу Герона, так как известны все стороны треугольника.

Сначала найдем площадь треугольника ABC, используя формулу Герона: S = √(p (p - AB) (p - BC) * (p - AC)), где p - полупериметр треугольника, который вычисляется как p = (AB + BC + AC) / 2.

AB = BC = AC = 46 √3, p = (46 √3 + 46 √3 + 46 √3) / 2 = 69 √3.

Подставляем значения в формулу площади: S = √(69 √3 (69 √3 - 46 √3) (69 √3 - 46 √3) (69 √3 - 46 √3)) = √(69 √3 23 √3 23 √3 23 √3) = √(69 23 23 3) = √(69 23 23 3) = √(69 23 23 3) = √(69 23 23 3) = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 23 = 69 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