Question

Стороны треугольника равняется 24 см 18 см и 8 см найти наибольший угол треугольника

Answer 1

Наибольший угол треугольника лежит против большей стороны. Большая сторона равна 24 см. Примем искомый угол равным α
По т.косинусов 
576=324+64-2•18•8•cosα
cosα=252:(-18•16)=-7/8
Наибольший угол arccos 7/8 или arccos -0,875 ( это угол 151°}

Answer 2

Finding the Largest Angle of a Triangle

To find the largest angle of a triangle, we need to determine the relationship between the lengths of the sides. Let's consider the given lengths of the sides of the triangle: 24 cm, 18 cm, and 8 cm.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This theorem helps us determine the type of triangle based on the lengths of its sides.

Let's analyze the given lengths of the sides:

- Side 1: 24 cm - Side 2: 18 cm - Side 3: 8 cm

Based on the triangle inequality theorem, we can determine that this triangle is valid because the sum of the lengths of any two sides is greater than the length of the third side:

- Side 1 + Side 2 = 24 cm + 18 cm = 42 cm > Side 3 - Side 2 + Side 3 = 18 cm + 8 cm = 26 cm > Side 1 - Side 3 + Side 1 = 8 cm + 24 cm = 32 cm > Side 2

Now, let's find the largest angle of the triangle. To do this, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

The Law of Cosines states that for a triangle with sides of lengths a, b, and c, and an angle opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we can label the sides of the triangle as follows:

- Side a: 24 cm - Side b: 18 cm - Side c: 8 cm

Let's calculate the largest angle using the Law of Cosines:

8^2 = 24^2 + 18^2 - 2 * 24 * 18 * cos(C)

Simplifying the equation:

64 = 576 + 324 - 864 * cos(C)

64 = 900 - 864 * cos(C)

864 * cos(C) = 900 - 64

864 * cos(C) = 836

cos(C) = 836 / 864

cos(C) ≈ 0.9676

To find the largest angle, we need to find the inverse cosine (arccos) of 0.9676:

C ≈ arccos(0.9676)

Using a calculator, we find that the approximate value of C is 14.5 degrees.

Therefore, the largest angle of the triangle is approximately 14.5 degrees.

Please note that the calculations provided are based on the given lengths of the sides of the triangle. If there are any errors or discrepancies in the given lengths, the results may vary.