Question

Навколо прямокутного трикутника ABC з прямим кутом С описано коло знайти радіус кола якщо АС=12 , /B=30°

Answer 1

Ответ:

R = 12 ед.

Объяснение:

Центр описанной около прямоугольного треугольника окружности лежит на гипотенузе и  ее радиус равен половине гипотенузы (свойство).

В прямоугольном треугольнике против угла 30° лежит катет, равный половине гипотенузы. Следовательно, R = 12 ед.

Answer 2

Finding the Radius of the Circumscribed Circle

To find the radius of the circumscribed circle of a right triangle ABC with a right angle at C, we can use the properties of a right triangle and the inscribed circle.

Given: - AC = 12 - ∠B = 30°

To find the radius of the circumscribed circle, we need to find the length of the hypotenuse AB and then divide it by 2.

Finding the Length of the Hypotenuse AB

We can use the trigonometric relationship between the sides and angles of a right triangle to find the length of the hypotenuse AB.

In a right triangle, the sine of an acute angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse. In this case, we can use the sine of ∠B to find the length of AB.

The sine of ∠B is given by:

sin(∠B) = opposite / hypotenuse

Since we know that ∠B = 30° and AC is the opposite side, we can rewrite the equation as:

sin(30°) = AC / AB

Simplifying the equation, we have:

1/2 = 12 / AB

To solve for AB, we can cross-multiply:

AB = 12 / (1/2) = 24

Finding the Radius of the Circumscribed Circle

Now that we know the length of the hypotenuse AB is 24, we can find the radius of the circumscribed circle by dividing AB by 2:

Radius = AB / 2 = 24 / 2 = 12

Therefore, the radius of the circumscribed circle is 12.

Please note that the sources provided did not contain specific information about the problem at hand. However, the solution is derived from the properties of right triangles and the relationship between the sides and angles.