Question

Сторони трикутника 5 м, 6 м, 7 м. Знайти висоту трикутника проведену до сторони довжиною 6 м.

Answer 1

Высота к стороне 6 м равна:
h = 2√(p(p-a)(p-b)(p-c))/6.
Полуппериметр р = (5+6+7)/2 = 18/2 = 9 м.
h =2√(9*4*3*2)/6 = 2√216/6 = 2*3√24/6 = √24 ≈ 4,89898 м.

Answer 2

В треугольнике ABC:

AB = 5
AC = 6
BC = 7
BE - высота, опущенная на сторону AC
AE + CE = 6 
AE = 6 - CE

В прямоугольном треугольнике ABE:
AE u BE - катеты
Гипотенуза AB = 5
По теореме Пифагора:
AB² = AE² + BE²
BE² = AB² - AE²

В прямоугольном треугольнике BCE:
BE u CE - катеты
Гипотенуза BC = 7
По теореме Пифагора:
BC² = BE² + CE²
BE² = BC² - CE²

⇒ AB² - AE² = BC² - CE²
5² - (6 - CE)² = 7² - CE²
25 - 36 + 12CE - CE² = 49 - CE²
12CE = 49 + 11
12CE = 60
CE = 5 (м)

По теореме Пифагора:
BC² = BE² + CE²
BE² = BC² - CE²
BE² = 7² - 5²
BE² = 49 - 25
BE² = 24
BE = √24
BE = 2√6 (м)

Answer 3

Calculating the Height of a Triangle

To find the height of a triangle drawn to the side of length 6 m in a triangle with sides of 5 m, 6 m, and 7 m, we can use the formula for the area of a triangle and the formula for the height of a triangle.

The area of a triangle can be calculated using the formula: Area = (1/2) * base * height

The height of a triangle can be calculated using the formula: Height = (2 * Area) / base

Calculation

Using the given side lengths of the triangle (5 m, 6 m, and 7 m), we can calculate the area of the triangle using Heron's formula and then find the height drawn to the side of length 6 m.

The semi-perimeter of the triangle, s, is calculated as: s = (5 + 6 + 7) / 2 = 9

The area of the triangle, A, can be calculated using Heron's formula: A = √(s * (s - 5) * (s - 6) * (s - 7)) A = √(9 * (9 - 5) * (9 - 6) * (9 - 7)) A = √(9 * 4 * 3 * 2) A = √(216) A ≈ 14.7 m²

Now, we can find the height drawn to the side of length 6 m: Height = (2 * 14.7) / 6 Height ≈ 4.9 m

So, the height of the triangle drawn to the side of length 6 m is approximately 4.9 meters.