Question

В треугольнике АВС угол С равен 90 градусов, угол А равен 30 градусов. Найти катеты.

Answer 1

Чтоб найти катеты нужно знать гиппотенузу.

Пусть гиппотенуза равна Х.

Тогда катет ВС, лежащий против угла А=30° равен половине гиппотенузы, т.е. ВС=Х/2

Катет АС лежащий против угла В равен: АС=(X√3)/2

это высчитывается либо по теореме Пифагара или через соs30°=(√3)/2

Answer 2

Problem Analysis

We are given a triangle ABC with angle C equal to 90 degrees and angle A equal to 30 degrees. We need to find the lengths of the legs (or catheti) of the triangle.

Solution

To solve this problem, we can use trigonometric ratios. In a right triangle, the sine, cosine, and tangent of an angle can be used to relate the lengths of the sides.

Let's denote the length of side AB as c, the length of side BC as a, and the length of side AC as b.

Using the given information, we have: - Angle C = 90 degrees - Angle A = 30 degrees

We can use the following trigonometric ratios: - Sine (sin): sin(A) = opposite/hypotenuse - Cosine (cos): cos(A) = adjacent/hypotenuse - Tangent (tan): tan(A) = opposite/adjacent

Since angle C is 90 degrees, side AB is the hypotenuse of the triangle.

Using the cosine ratio, we can find the length of side BC: cos(A) = BC/AB cos(30) = BC/c BC = c * cos(30)

Using the sine ratio, we can find the length of side AC: sin(A) = AC/AB sin(30) = AC/c AC = c * sin(30)

Calculation

Let's calculate the lengths of the legs of the triangle.

Using the cosine ratio: BC = c * cos(30)

Using the sine ratio: AC = c * sin(30)

Answer

The lengths of the legs of the triangle ABC are: - BC = c * cos(30) - AC = c * sin(30)

Please note that we don't have the length of the hypotenuse (AB) or any other information about the triangle, so we cannot determine the exact lengths of the legs without additional information.

Let me know if there's anything else I can help you with!