Question

Знайти радіус кола, описаного навколо трикутника АВС, якщо ВС=12 коренів з 2, кут А=45'

Answer 1

Радиус окружности, описанной вокруг треугольника находится по следствию из теоремы синусов: $\frac{a}{sin \alpha } =2R$, тогда в данной задаче получаем:
$2R= \frac{12 \sqrt{2} }{sin 45^{0} } = \frac{12 \sqrt{2} }{ \frac { \sqrt{2} }{2} } =24$. Итого, R=12.

Answer 2

Finding the Radius of the Circumscribed Circle

To find the radius of the circle circumscribed around triangle ABC, we can use the following steps:

1. Given Information: - BC = 12√2 - ∠A = 45°

2. Using Trigonometric Relations: - The radius of the circumscribed circle can be found using the formula: R = a / (2sinA), where R is the radius of the circumscribed circle, a is the side opposite the angle A, and A is the angle of the triangle.

3. Calculating the Radius: - In this case, the side opposite angle A is BC, so we can use the given value of BC to calculate the radius.

- Using the formula R = BC / (2sinA), we can substitute the given values: R = 12√2 / (2sin45°)

4. Calculation: - Simplifying, we get: R = 12√2 / (2 * (1/√2)) R = 12

Conclusion

The radius of the circle circumscribed around triangle ABC is 12. This is calculated using the given side length BC and the angle A of the triangle.