Question

Find the relation between the length of a side and the circumradius of an equilateral triangle.​

Answer 1

Answer:

By sine rule, a/sin A = b/sin B = c/sin C = 2R for any triangle, where R represents the circumradius of the triangle. For an equilateral triangle, a=b=c and A=B=C=60°

By sine rule, a/sin A = b/sin B = c/sin C = 2R for any triangle, where R represents the circumradius of the triangle. For an equilateral triangle, a=b=c and A=B=C=60°Hence a/sin 60° = 2R

By sine rule, a/sin A = b/sin B = c/sin C = 2R for any triangle, where R represents the circumradius of the triangle. For an equilateral triangle, a=b=c and A=B=C=60°Hence a/sin 60° = 2Ra/(√3/2) = 2R and therefore a = √3 R

Answer 2

Answer:

One side of an equilateral triangle is √3 times its circumradius.

Circumscribed circle of an equilateral triangle is made through the three vertices of an equilateral triangle. The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where 'a' is the length of the side of equilateral triangle.