Answer:
The diameter of the circumscribed circle is 6.92
Step-by-step explanation:
In the question, we are asked to calculate the diameter of a circle, which has a an equilateral triangle inscribed in it.
To solve this problem, let us consider the diagram attached.
Now let’s assume the point o is the center of the circle and that r is the radius of the circle. Now to calculate this radius, we need to employ the use of a trigonometrical ratio.
According to the question, we can see that we have the adjacent and the hypotenuse, so the trigonometric identity to use is the cosine.
Mathematically;
Cosine 30 = 3/r
r = 3/cosine 30
Cosine 30 = 0.866
r = 3/0.866
r = 3.46
But in the question, we were asked to calculate the diameter and not the radius.
Mathematically; d = 2r = 2 * 3.46 = 6.92
