Question

An equilateral triangle with sides of length 6 is inscribed in a circle what is the diameter

Answer 1

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