Question

An equilateral of sidewalk 20cm is lnscribed in a circle calculate the distance of a side of the triangle from the center of the circle

Answer 1

each side of the triangle intersects a 120 degree or (2 pi/3) radian arc of the circle. Look at hypotenuse and altitude of triangle from center of circle to center of side

sin 60 = 10/R so R = 10/sin 60 = 20 /sqrt 3
sin 30 = h/R = 1/2
so h = R/2 = 10/sqrt 3