Question

У трикутнику АВС відомо, що АВ=8см,кут С= 30 градусов,кут А=45 градусіів.знайти сторону ВС

Answer 1

Перевод на русский:
В треугольнике АВС известно, что АВ=8см, угол С= 30 градусов, угол А=45 градусов. Найти сторону ВС

По теореме синусов: 
ВС/sin45=AB/sin30
BC=AB*sin45 /sin30
BC=8 *√2/2 :1/2=4 *√2 *2=8√2

Ответ:ВС=8√2см

Answer 2

Problem Analysis

We are given a triangle ABC with the following information: - AB = 8 cm - ∠C = 30 degrees - ∠A = 45 degrees

We need to find the length of side BC.

Solution

To find the length of side BC, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant. The formula for the Law of Sines is:

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

In our case, we know the length of side AB (a = 8 cm), the measure of angle A (∠A = 45 degrees), and the measure of angle C (∠C = 30 degrees). We want to find the length of side BC (b).

Using the Law of Sines, we can set up the following equation:

8/sin(45) = b/sin(30)

Now, we can solve for b:

b = (8 * sin(30)) / sin(45)

Let's calculate the value of b using this equation.

Calculation

Using a calculator, we can find the value of sin(30) and sin(45):

sin(30) ≈ 0.5 sin(45) ≈ 0.707

Substituting these values into the equation, we get:

b = (8 * 0.5) / 0.707

Calculating this expression, we find:

b ≈ 5.657 cm

Therefore, the length of side BC is approximately 5.657 cm.

Answer

The length of side BC in triangle ABC is approximately 5.657 cm.