∆𝐴𝐵𝐶 is an equilateral triangle with a side length 12 inches. What is the height of ∆𝐴𝐵𝐶? Provide your answer in simplest radical form.

Answer 1

triangle with 3 sides each 12 inches, also has 3 angles each = 60 degrees= pi/3

slice the triangle down the middle, creating a right triangle with 12=hypotenuse,

and height = 12sin60 = 12sin(pi/3)

12sin60 = the height

sin60 = sqr3/2= opposite side over hypotenuse = height/12

height = 12(sqr3)/2 = 6sqr3 inches