Question

У трикутнику АВС кут А=60°, ВС=3 корінь 3см. Знайдіть радіус кола описанного навколо трикутника АВС.

Answer 1

Ответ:

3 см.

Объяснение:

По теореме в ∆АВС

2R = BC/sinA

В нашем случае

2R = 3√3 / sin60° = 3√3 : √3/2 = (3√3 • 2)/√3 = 6 (см).

R = 6 : 2 = 3 (см).

Answer 2

Problem Analysis

We are given a triangle ABC with angle A measuring 60 degrees and side BC measuring 3√3 cm. We need to find the radius of the circle circumscribed around triangle ABC.

Solution

To find the radius of the circumcircle, we can use the formula derived from the Law of Sines. The formula is as follows:

R = (a / (2 * sin(A)))

Where R is the radius of the circumcircle, a is the length of side BC, and A is the measure of angle A.

Substituting the given values into the formula, we have:

R = (3√3 / (2 * sin(60°)))

Now, let's calculate the value of sin(60°) and substitute it into the formula.

Using the trigonometric identity sin(60°) = √3 / 2, we have:

R = (3√3 / (2 * (√3 / 2)))

Simplifying the expression, we get:

R = 3 cm

Therefore, the radius of the circumcircle of triangle ABC is 3 cm.

Answer

The radius of the circumcircle of triangle ABC is 3 cm.