Answer: correct answer is B.
Step-by-step explanation:
in the small triangle
taking 60 as reference angle
b = [tex]10\sqrt{3}[/tex]
so
tan 60 = p/b
[tex]\sqrt{3}[/tex] = p/([tex]10\sqrt{3}[/tex])
30 = p
so
[tex]h^2 = p^2 + b^2\\ = 30^2 + (10\sqrt{3} )^2\\\\ = 900 + 300\\ = 1200\\so h^2 = 1200\\then, h = \sqrt{1200} \\ = 20\sqrt{3} \\so\\in bigger triangle\\\\h = x[/tex](taking 45 as reference angle)
so
in bigger triangle
b = 20[tex]\sqrt{3}[/tex]
so
tan 45 = p/b
1 = p/(20[tex]\sqrt{3}[/tex])
p = 20[tex]\sqrt{3}[/tex]
so h^2 = p^2 + b^2
so
h^2 = (20[tex]\sqrt{3}[/tex])^2 +( 20[tex]\sqrt{3}[/tex])^2
= 1200 + 1200
h^2 = 2400
h =[tex]\sqrt{2400}[/tex]
=20[tex]\sqrt{6}[/tex]
so x = 20[tex]\sqrt{6}[/tex]
