Answer:
x = 4[tex]\sqrt{3}[/tex] = 6.9
Step-by-step explanation:
if the large triangle is equilateral then each angle is 60°
but the altitude creates two smaller triangles that measure 30-60-90°
the ratio of sides, respectively, is 1 : [tex]\sqrt{2}[/tex] : 2
we can create a proportion to find 'x':
x/2 = [tex]\sqrt{12}[/tex]/1
cross-multiply:
x = 2[tex]\sqrt{12}[/tex]
since [tex]\sqrt{12}[/tex] = [tex]\sqrt{4}[/tex]·[tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex]
so 'x' = 2·2[tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]
therefore, we can see that the side opposite the 30° angle is half the hypotenuse