Question

№446 який кут трикутника abc найглибший а який найменший якщо: 1)ab=3м Bc=4м ac=5м 2)ab-bc=2м, bc-ac=1м? №449 чи існєує трикутник кожній кут якого більший за60 градусів ДАЮ40 БАЛЛОВ!

Answer 1

Объяснение:

449) ні, бо трикутник завжди має 180°

446)

аб=3м, бс=4м, ас=5м

у нас ніби 12 частин

12х=180

180:12=15

15×3=45°

15×4=60°

15×5=75

якщо не правильно, пробач

Answer 2

Triangle ABC - Finding the Largest and Smallest Angles

To determine the largest and smallest angles of triangle ABC, we need to analyze the given information.

1) When the lengths of the sides of a triangle are known, we can use the Law of Cosines to find the angles. The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c:

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

In this case, we have the following information: - ab = 3m - bc = 4m - ac = 5m

To find the angles, we can use the Law of Cosines for each angle. Let's calculate the angles:

- Angle A: - Using the Law of Cosines: a^2 = b^2 + c^2 - 2bc * cos(A) - Substituting the given values: 3^2 = 4^2 + 5^2 - 2 * 4 * 5 * cos(A) - Solving for cos(A): cos(A) = (4^2 + 5^2 - 3^2) / (2 * 4 * 5) - Calculating cos(A): cos(A) = 0.8 - Taking the inverse cosine (arccos) to find the angle: A ≈ 36.87°

- Angle B: - Using the Law of Cosines: b^2 = a^2 + c^2 - 2ac * cos(B) - Substituting the given values: 4^2 = 3^2 + 5^2 - 2 * 3 * 5 * cos(B) - Solving for cos(B): cos(B) = (3^2 + 5^2 - 4^2) / (2 * 3 * 5) - Calculating cos(B): cos(B) = 0.6 - Taking the inverse cosine (arccos) to find the angle: B ≈ 53.13°

- Angle C: - Using the Law of Cosines: c^2 = a^2 + b^2 - 2ab * cos(C) - Substituting the given values: 5^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(C) - Solving for cos(C): cos(C) = (3^2 + 4^2 - 5^2) / (2 * 3 * 4) - Calculating cos(C): cos(C) = -0.2 - Taking the inverse cosine (arccos) to find the angle: C ≈ 143.13°

Now that we have the measures of angles A, B, and C, we can determine the largest and smallest angles.

The largest angle is angle C, which measures approximately 143.13°. The smallest angle is angle A, which measures approximately 36.87°.

2) In the second scenario, we are given the differences between the sides of the triangle:

- ab - bc = 2m - bc - ac = 1m

Unfortunately, with only the differences between the sides, we cannot determine the exact measures of the angles. We would need additional information, such as the lengths of at least one side or one angle measure, to solve for the angles.

Therefore, we cannot determine the largest and smallest angles of triangle ABC based on the given differences between the sides.

Triangle with Angles Greater than 60 Degrees

In question number 449, we are asked if a triangle exists where each angle is greater than 60 degrees, with one angle measuring 40 degrees.

To determine if such a triangle exists, we need to consider the sum of the angles in a triangle. In any triangle, the sum of the three angles is always 180 degrees.

Let's analyze