Question

Найдите неизвестные элементы треугольника АВС, если: b= 4,5, угол A=30°, угол C=75°. помогите пожалуйста срочно!​

Answer 1

Ответ и решение на фото (не полный как считать стороны я не знаю)

Answer 2

Given Information:

We are given the following information about triangle ABC: - Side b = 4.5 - Angle A = 30° - Angle C = 75°

Solution:

To find the unknown elements of triangle ABC, we can use the properties of triangles and trigonometry.

Finding Side a:

We can use the Law of Sines to find side a. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In other words:

a / sin(A) = b / sin(B) = c / sin(C)

Since we know side b and angle A, we can rearrange the formula to solve for side a:

a = (b * sin(A)) / sin(B)

Substituting the given values, we have:

a = (4.5 * sin(30°)) / sin(B)

To find angle B, we can use the fact that the sum of the angles in a triangle is 180°:

Angle B = 180° - Angle A - Angle C

Substituting the given values, we have:

Angle B = 180° - 30° - 75°

Now we can calculate side a using the formula:

a = (4.5 * sin(30°)) / sin(B)

Let's calculate the value of side a and angle B.

Calculation:

Using a calculator, we find that sin(30°) ≈ 0.5.

Substituting the values into the formula, we have:

a = (4.5 * 0.5) / sin(B)

To find sin(B), we can use the fact that the sum of the angles in a triangle is 180°:

sin(B) = sin(180° - Angle A - Angle C)

Substituting the given values, we have:

sin(B) = sin(180° - 30° - 75°)

Using a calculator, we find that sin(75°) ≈ 0.9659.

Substituting the value of sin(B) into the formula, we have:

a = (4.5 * 0.5) / 0.9659

Calculating the value of side a, we get:

a ≈ 2.318

Therefore, side a is approximately 2.318.

Finding Angle B:

Now that we have the values of sides a and b, we can use the Law of Sines to find angle B. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In other words:

a / sin(A) = b / sin(B) = c / sin(C)

Since we know sides a and b, we can rearrange the formula to solve for angle B:

sin(B) = (b * sin(A)) / a

Substituting the given values, we have:

sin(B) = (4.5 * sin(30°)) / 2.318

Calculating the value of sin(B), we get:

sin(B) ≈ 0.974

To find angle B, we can use the inverse sine function:

Angle B = sin^(-1)(0.974)

Using a calculator, we find that:

Angle B ≈ 76.6°

Therefore, angle B is approximately 76.6°.

Summary:

Based on the given information, we have found the following unknown elements of triangle ABC: - Side a ≈ 2.318 - Angle B ≈ 76.6°

Please note that these values are approximate due to rounding.

I hope this helps! Let me know if you have any further questions.