Question

Стороны треугольника ABC: AB=1 см AC=7√3 BC=13см найдите наибольший угол треугольника ABC​

Answer 1

Объяснение:

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Answer 2

Finding the Largest Angle of Triangle ABC

To find the largest angle of triangle ABC, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides of lengths a, b, and c, and opposite angles A, B, and C respectively, the following equation holds:

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

In this case, we are given the lengths of sides AB, AC, and BC. Let's substitute the given values into the equation and solve for angle C, which is the largest angle of triangle ABC.

Given: - AB = 1 cm - AC = 7√3 cm - BC = 13 cm

Using the Law of Cosines, we have:

BC^2 = AB^2 + AC^2 - 2 * AB * AC * cos(C)

Substituting the given values:

13^2 = 1^2 + (7√3)^2 - 2 * 1 * 7√3 * cos(C)

Simplifying:

169 = 1 + 63 - 14√3 * cos(C)

168 = 14√3 * cos(C)

Dividing both sides by 14√3:

cos(C) = 168 / (14√3)

To find the value of cos(C), we can simplify it further:

cos(C) = 12 / √3

Now, we can find the value of angle C by taking the inverse cosine (arccos) of cos(C):

C = arccos(12 / √3)

Using a calculator, we can find the value of C to be approximately 15.26 degrees.

Therefore, the largest angle of triangle ABC is approximately 15.26 degrees.