Answer:
[tex]3\sqrt{6}[/tex]
Step-by-step explanation:
so first the triangle on the left has 90 degrees and 45 degrees. this means the third missing angle is 45 degrees, making it an isosceles triangle
keep in mind that the 2 side lengths (not hypotenuse are the same)
use Pythagorean theorem
[tex]9^2 = a^2 +b^2[/tex]
and a=b because the lengths are equal
so [tex]81= 2a^2[/tex]
40.5= [tex]a^2[/tex]
a= [tex]\sqrt{40.5[/tex]
the triangle on the right is a 30 60 90 triangle
thus its side lengths are in a special ratio, see screenshot attached
[tex]\sqrt{40.5}[/tex] is between 90 and 30 degrees so it is [tex]a\sqrt{3}[/tex] where a is common factor
find a
[tex]\sqrt{40.5} =a\sqrt{3} \\a=\sqrt{13.5} \\a= -\sqrt{13.5}[/tex]
not negative because in context this is geometry there are no negative lengths
so a= [tex]\sqrt{13.5}[/tex]
x in this 30 60 90 triangle is 2a
so [tex]2*\sqrt{ 13.5}[/tex]
which is equal to [tex]3\sqrt{6}[/tex]
please mark brainleist lol
hope this helps !! gl
