Step-by-step explanation:
In a normal triangle, there is a formula as following:
+) cosine of an angle = [tex]\frac{Adjacent side 1^{2}+Adjacent side 2^{2} - Opposite side^{2}}{2*Adjacent side 1 * Adjacent side 2}[/tex]
Angel B = 30° has:
+) 2 adjacent sides: BC and AB
+) Opposite side: AC
=> We have:
cosine ∠B = [tex]\frac{BC^{2}+AB^{2}-AC^{2} }{2*AB*BC}[/tex]
=> cosine 30° = [tex]\frac{(2\sqrt{3})^{2} + 4^{2} - AC^{2} }{ 2 *4*2\sqrt{3} }[/tex]
=> [tex]\frac{\sqrt{3} }{2} = \frac{28 - AC^{2} }{16\sqrt{3} }[/tex]
=> 2 x (28 - AC^2) = 48
=> AC^2 = 4
We have:
[tex]BC^{2} = (2\sqrt{3} )^{2} =12[/tex]
[tex]AB^{2} = (4 )^{2} =16[/tex]
[tex]AC^{2} = 4[/tex]
=> [tex]AC^{2} +BC^{2} = AB^{2}[/tex]
According the inverse Pythagorean theorem, ABC is the right angle triangle with Angle ACB = 90°
=> X + 30 = 90
=> X = 60°