Question

В треугольнике ACB сторона AB=12 см,а угол ACB=30 градусов.найдите радиус описанной окружности?

Answer 1

12/sin30=2R
sin30=1/2
2R=24
r=12

Answer 2

Problem Analysis

We are given a triangle ABC with side AB measuring 12 cm and angle ACB measuring 30 degrees. We need to find the radius of the circumcircle of triangle ABC.

Solution

To find the radius of the circumcircle, we can use the formula:

Radius of circumcircle = (side AB) / (2 * sin(angle ACB))

Substituting the given values, we have:

Radius of circumcircle = 12 cm / (2 * sin(30 degrees))

Now, let's calculate the value of sin(30 degrees) using a calculator or trigonometric table.

Using the value of sin(30 degrees), we can calculate the radius of the circumcircle.

Calculation

Using the value of sin(30 degrees) = 0.5, we have:

Radius of circumcircle = 12 cm / (2 * 0.5) = 12 cm / 1 = 12 cm

Therefore, the radius of the circumcircle of triangle ABC is 12 cm.

Answer

The radius of the circumcircle of triangle ABC is 12 cm.