Question

Сторони трикутника мають довжини 8 см, 18 см і 24 см. Знайти менший кут трикутника

Answer 1

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Answer 2

Finding the Smallest Angle of a Triangle

To find the smallest angle of a triangle with sides of lengths 8 cm, 18 cm, and 24 cm, we can use the law of cosines. The law of cosines states that in a triangle with sides of length a, b, and c, and angles opposite those sides A, B, and C, the following equation holds true:

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

We can use this equation to find the smallest angle of the triangle.

Using the law of cosines, we can calculate the smallest angle of the triangle using the given side lengths. Let's proceed with the calculation.

First, we need to identify the smallest side of the triangle. Then, we can use the law of cosines to find the smallest angle.

The smallest side of the triangle is 8 cm. Using the law of cosines, we can calculate the smallest angle as follows:

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

Substituting the values: a = 18 cm b = 24 cm c = 8 cm

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

Let's calculate the value of cos(C) using the given formula.

cos(C) = (18^2 + 24^2 - 8^2) / (2 * 18 * 24) cos(C) = (324 + 576 - 64) / (864) cos(C) = 836 / 864 cos(C) ≈ 0.96875

Now, we need to find the angle whose cosine is approximately 0.96875. We can use the inverse cosine (arccos) function to find this angle.

C ≈ arccos(0.96875) C ≈ 14.47 degrees

Therefore, the smallest angle of the triangle is approximately 14.47 degrees.