Question

У трикутнику АВС кут С=90 кут В=30 АВ =4 см Знайдить АС​

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

Problem Analysis

We are given a triangle ABC with angle C equal to 90 degrees, angle B equal to 30 degrees, and side AB equal to 4 cm. We need to find the length of side AC.

Solution

To find the length of side AC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the length of side AC as c. According to the Pythagorean theorem, we have the following equation:

c^2 = a^2 + b^2

where a is the length of side AB and b is the length of side BC.

We are given that angle B is 30 degrees, which means that angle A is 90 - 30 = 60 degrees. Since the sum of the angles in a triangle is always 180 degrees, angle C is 180 - 90 - 60 = 30 degrees.

Now, we can use trigonometric ratios to find the lengths of sides BC and AC.

Using the sine function, we have:

sin(B) = BC / AB

sin(30) = BC / 4

BC = 4 * sin(30)

Using the cosine function, we have:

cos(B) = AC / AB

cos(30) = AC / 4

AC = 4 * cos(30)

Now, we can substitute the values of sin(30) and cos(30) to find the lengths of sides BC and AC.

Calculation

Let's calculate the values of BC and AC using the given information.

BC = 4 * sin(30) = 4 * 0.5 = 2 cm

AC = 4 * cos(30) = 4 * (√3 / 2) = 2√3 cm

Therefore, the length of side AC is 2√3 cm.

Answer

The length of side AC in triangle ABC is 2√3 cm.

Explanation

In triangle ABC, we are given that angle C is 90 degrees, angle B is 30 degrees, and side AB is 4 cm. Using the Pythagorean theorem and trigonometric ratios, we can find the length of side AC. By substituting the values, we find that the length of side AC is 2√3 cm.